Things she's created/built in the past:
Daxamite Iron sickness cure
Brainy found records of her great grandfather having created a temporary cure for the Daxamite Iron sickness, and perfected it for Andromeda. The cure she tweaked is a permanent solution, and tailored for the individual. This means that not all Daxamites can take the cure. It must be altered to suit them alone. To take this cure without that brings insanity.
Valorium - Flight metal
This is the component that allows the flight rings to work. Querl invented it in her teens, and Legion has made the most of it. The metal naturally floats and takes mental direction if worn. A tiny sliver can lift two or more people at the merest mental command. And yes, she can create more. She's just not sure she should in the 21st century.
As silly as it is, she did once create a shrink ray. Because she was bored.
This is a creation of Barry Allen, but Querl has built and improved on the design a couple of times during her membership with Legion. She knows very well how it works and what it does.
Querl perfected time travel when she was seventeen, and all because she wanted to see the face of her mother. Not to change the past, which she knew was bad to try already, but merely to know what her mother looked like. The platform worked, but was never used beyond some trial testing. Querl was also jailed for having created it.
Think holoroom from Star Trek, but with a twist. The anywhere room used holotechnology to allow for safe exploration of other worlds. Using scans of other worlds, and even subatomic environments, the anywhere room put real time projections of people in those environments. People inside could interact to a degree with the environment without any risk to either.
Created by RJ Brande industries, Querl wasn't a part in creating this gate network, but she knows in detail how it functions, and has worked repairs on it in the past. The problem with this network is that she can't create the very necessary component (tarnium) that allows it to function. In fact, no one will be able to create it for another seven hundred years or so because the Trommites don't exist yet.
This engine is entirely Querl's design and something she can recreate. A ship that allows for vast areas of space to be covered by folding space. She built it out of the remains of the Legion Outpost when half the team was 'lost'.
This is another form of gate technology that can allow one to travel anywhere in space. The problem with this is, is that one must have a guide to utilize it and the only guides who can do this don't quite have the means yet. So it's not truly viable technology at this time.
Much to her regret, Querl knows very well what these are, and how they function. She acquired a sample of the crystals once and hid the fact she had them. Then they began to grow. Several Legionnaires, including herself, were transformed into Bizzaros. In as much as Lyle saved everyone, Querl won't be playing with these things again if she can help it.
As the weeks pass, and staff approve things, Querl's going to acquire a wealth of nifty widgets. This is where I'll keep them.
While it is only one bed, this is what amounts to a full medical facility. It creates a sterile area around it, and works under nearly thirty first century technology recreated by Querl. This means that while it can't quite do everything, it can run detailed scans down to genetic levels and beyond, work wondrous cures, and do intricate surgeries without exposing the patient to infection. It has been programmed with knowledge of the body that human doctors on Earth may not currently be aware of, and is familiar with sicknesses not of Earth origin. As well as most of those on Earth. (Querl adds in what she finds, but there are gaps in it's knowledge base at this stage.) Now, that said, the bed doesn't operate autonomously. It requires someone trained in it's use to active the necessary chain of systems. It it not a robot and can not determine things on its own.
Red Sun Lamp
This very simple device can even be made by 21st century technology. Literally all it does is simulate the light of a red sun. The reason for this is for Daxamites and Kyptonians. Shine this light on them and it temporarily removes their powers. This makes the tending to injuries possible. Querl keeps it quite hidden a lot of the time so that it isn't stolen and used for nefarious purposes.
A personal computer from the future, Querl carries at least two of these at all times. Hers are also of her own design. Sure they look like a Brande 5k model, but inside they are vastly different. Omnicoms are powerful computers, and Querl's is that much more. She can run diagnostics with it, scan environments, uplink with compatible systems.. a lot. Problem is, she's only two, and lacks the materials to replace them if they are damaged beyond repair.
These nifty things are what do the holoscreens that she's shown creating in RP.
This ring has on it the symbol of the Legion, and beyond signifying membership, it has a few other uses as well. It allows the wearer to fly at good speeds, in atmosphere and space even to the point of carrying others. The ring also allows communication with other Legionnaires, and lets other Legionnaires locate the wearer, through the hyperspace communicator and sub-space transmitter beacon contained in each ring. The last bit of awesomeness is that it also protects the wearer in space, and other environmental conditions. Querl's ring has been carefully attuned to her own biometrics. It can not be used by others, and she can control it from a short distance.
Ear Plug communicator
The communicator of course allows for communication, but it does so in a number of ways. Hyperspace communications, telepathic means, and it even translates if given the proper language information.
An important thing to remember about Querl is that she learns.. everything. (Excepting perhaps social skills, but that's another story.) That's why things are so generalized here. They have to be. If I were to write out each and every skill there'd be dozens of skill listings. You could almost say that her greatest power is the ability to learn. Anything and everything. What limits her is her own desire. She could be an amazing combatant considering her ability to control her own body, and yet she refuses to do more than learn the bare basics of brawling.
Thanks to the telepathic earplugs, the Legion doesn't often need to learn any languages, but for Brainiac languages are something she enjoys learning. While she doesn't know all languages, she knows far too many to name here, and if she doesn't know it, she can learn it in a distressingly short amount of time. Mere minutes if the situation allows. Even ancient Latin, to the common languages of her own era.. Querl can speak it. (A special note here is Kryptonian. Querl can speak it.) Querl knows hundreds and hundreds of languages.
If she's heard it, read it, or some other strange means.. it's trapped there in her memory. This trait is to sum up the incredible wealth of information Querl has. Most of it is completely useless, but occasionally it's something she needs. Kind of hard to describe this since it covers so much. Just that she knows things about just about everything. An example is in Legion Lost when Brainy recognizes a centipede as being Chameleon because the breed wasn't native to Metropolis.
I lump all this together because Querl knows so much there's no point in in attempting to divide it up. If it's done with technology, she can figure it out. Figure it out, use it to it's best capabilities, upgrade it, change it, shape it to her needs, and explain it in such detail anyone listening would consider fleeing just to escape the over load of information. She is of course limited to what she has on hand. Without any means of technology her options grow more limited. Computers, machines, vehicles.. anything that figures under technology. And yes she can pilot, or drive, anything you put her in if she has a few moments to learn it. Not that she's a great driver, but hey.
Like technology, this trait is because she knows so much. Chemistry, biology, genetics, astronomy, mathematics.. the list goes on and on. It's not that she's a master of every field, for there are certainly others who know more about specific subjects, but Querl knows a great deal about all of them. (Like Lyle knows more of biology.)
Something she loves to learn about. She knows details and events that others never bothered with, or had forgotten. Really, she's a walking library in a lot of ways. While Querl doesn't know everything about all worlds, she does her best to remedy such a lack if ever where's the opportunity. An example of this is the Robotica. She knew that the robots had been shut down and were used as ballast in old freighters when most people hadn't even heard of the trouble said robots had started.
While this could be lumped into science, I felt that it should be separate. Querl isn't a doctor, and yet she's the one that normally gets stuck healing people when trouble hits. From Jan's blindness, to Dirk's trouble with being radioactive.. she's called upon when the team thinks 'normal' medical staff can't handle it. Maybe she should get around to getting a doctorate. (If she already hasn't.)
While Querl has no official training, she none the less has had several years of being forced to fight. And with how well the Coluan leans, she's actually quite good at it. Especially with her force field. That's how she survives so many combats, and it's her main weapon.
While not something she willingly does, Querl does in fact know a good deal about the arcane. The majority of this is lore, for she's avoided the application aspect. Still, while magic is a dirty word, the Coluan does know a good deal about it. More than the common person, but certainly not as much as a practitioner.
Something well within human ability, Querl's sheer intellect, and force of will, allows her to control her own body to a certain degree. An example would be forcing her body to release adrenaline when it's necessary, or regulating her own temperature. She can tell if a wound is clotting just by feel (For all she couldn't stop the bleeding), calm her heart rate, force herself to stay awake long past the time a normal person could, or even sleep in an instance, anywhere. There are monks in Tibet who have mastered such things by use of meditation. It is something documented and studied by science. Querl doesn't practice their meditations, but does it by over riding her own system by simply being too damn smart, and stubborn, for her own good.
The Coluan people have a life span of five hundred to seven hundred years on the average. Unless being a Legionaire, or one of the many as of yet unknown remnants of her family history, kill her, Querl is going to be around for a very, very long time.
Gift of Invention
Intelligence does not mean one has the ability to invent, and invention does not always mean genius. Querl has both in spades. How else is she able to cobble together the things that she does? While this also doesn't signify creativity, for other Legionaires are more imaginative, she none the less has the ability to see possibilities that others don't, and then to make that image into reality. With out this quirk, Querl wouldn't be able to do the incredible things she does time and time again for the Legion. Invent a FTL drive out of scrap? Just give her time and materials. (Problem is getting materials.)
Querl really does believe in magic. She's been at the receiving end of it too many times not to accept its reality. That doesn't mean she has to like it though. Querl would be only too happy to never have to deal with magic ever again, and she goes out of her way to avoid it. See, years ago Querl actually worked magic for a brief time. It was only one spell, but she researched it, figured out how it worked using mundane materials, and cast a spell all on her own. Damn thing worked too!
The problem was is that all magic has a price. That's a part of how magic works. She even got off lucky in that the price was only her pride. And she knows it. That's part of what scares her about magic. The price was too high for what she did. That's why she sticks with technology. It has set rules, easily seen boundaries, and doesn't always have an uncomfortable cost.
The flaw? Once you use magic it comes back to haunt you. It's only a matter of time.
Lack of foresight
Querl just doesn't always think things through all the time. Especially when she's working. She gets so excited, so focused, that she doesn't think about what the finished product might do. Or what would happen if she fails. Too much excitement and not enough restraint. (Computo anyone?)
The Brainiacs aren't exactly known for their good deeds. An understatement to be sure. While Querl is the black sheep of the family in that she's done more good then evil, that doesn't change a thousand years of conquests, out right evil, and shady doings. There are going to be ..things out there just waiting to get back at Brainiac. Dangerous things that want her dead merely because of the family she was born into. It will bring her fear and distrust at the very least.
You can't pick your family. Querl's is anything but pleasant, and she'll always being a victim to her own genetics. While it hasn't been a problem for Brainiac 5 in full, she is descended from a line of highly unstable, and often psychopathic, villains. It shows in little ways, such as her mood swings, and lack of ability to think of the consequences of her own actions, but this time bomb lays within her waiting to be set off.