Is it possible to make something like this interesting? How do I proceed from here? Example:
Anxiety & Depression
Makes other people feel what you are feeling. It's more fun with friends. You just appear and suddenly the enemy is feeling hopeless.
Multiple Personality Disorder
Manifests the different personality as clones that can act independently from the user.
Schizophrenia
Turns selected hallucination and delusion into reality.
Any thoughts? This isn't a cry for help.
Alright, I'm home, on a keyboard, so I can actually give this more thought.
First off, do your research, and interview with people. In order to write people with illness with powers, you must first be able to write people with illness. Otherwise it will not work.
Second, based on your title, it sounds like you want the illness to be what grants the power. This... this is dangerous territory. I think it can be done, and if you're truly passionate, and dedicated, you can do it and do it well, but be forewarned; you will be under scrutiny, and you will be under scrutiny from people who have different standards, so you're likely to piss someone off no matter what you do.
Let's say you accept the risk and want to continue, and you've done your interviewing. What I would do is make the universe itself powered, and have the mental illnesses confer additional modifications. The main reason I say this is you bring up
anxiety and
depression. Anxiety is a double-edged sword, but Depression doesn't bring anything to the picture. It just kinda... sits there. It's an all-encompassing rut that people have to throw spoons at in order to
do anything. (Okay Spoon Theory holds that depressed people have
less spoons, but the math works out the same way if you assign the same number of spoons and then assign a block). For this reason I will separate the two and describe them differently. I will assume all people with X illness have Y powers, instead of it just being the MC.
Anxiety
Anxiety I feel is the most double-edged of them all. Anxiety is always being on the lookout, being nervous, not able to bring out your best self. And this would manifest in your powers. You kick into fight/flight a lot, and find it really hard to overcome adversity and push through. I like TrashyHuman's idea of slowing down your perception of time, but we can expand on this. I imagine in this world there are low-level powers that are short and sweet, and high-level powers that are stronger but require more "cast time" and other resource expenditure. I would give Anxiety the power-up of increasing the speed and potency of your low-level powers. Mayhaps it slows down your perception of time so you can fine-tune all the things you need to do to release them, and you just don't have the patience to wait out the full time. If you take Pathfinder, imagine it this way: You can barely cast Fireball, and Disintegrate is right out. But you have Magic Missile, and a LOT of Magic Missile. You can even justify it this way: your energy reserve for powers keeps overfilling because you never use your strong powers because you trip over yourself, so it just kinda bleeds out, but you can use that bleedover to throw lots of cantrips, faster than other people. You're still anxious, though!
Depression
The real reason I want more than one person to have powers. If you've worked with someone with Depression, it's hard to motivate them. Let's take that theme and extend it to these powers:
You resist heavily or are immune to Powers. Like that's it. It works because Powers are a mental thing, and that's because you're deriving the Power from the Illness. And it reflects real life because persuading someone to do anything is a mental power too, it's just a mundane one that we have IRL.
Multiple Personality Disorder more currently known as Dissociative Identity Disorder
K5Rakitan is right; the name has changed, and if you're looking for resources, you will want to do so under the disorder's current name as it reflects more current understanding. Old research has data and that data is still important, but it's "deprecated" in that it might be contradicted by new information, and the new information is understood to win out. The basic idea is this: your mindscape is divided into multiple distinct identities, selves, consciousnesses, etc. The thing is this: The different consciousnesses, formally called alters, need not want the same thing nor have the same mental abilities. In fact it's not uncommon for alters to be opposed to each other, which is why it's a problem for those afflicted with it. So here's what I would do, and actually ended up doing in my own work, Solstice: Your alters have different powers (In Solstice, I don't have anyone with DID currently, but there are people who literally have two spirits within their body, each with its own magic). Boom. done. If you are operating as Alice (or, to put it in standard terms, if Alice is fronting, meaning has command of the body), then you have Alice's mental abilities, including whatever powers she has. Now when you switch to Bob, you have Bob's mental abilities, but also his goals and aspirations. Note that this swap IS NOT OFTEN VOLUNTARY! In fact, the act of me saying "you" to refer to the complete physical being (normally called a System) will ruffle some feathers in itself, but that is an outsider's perspective: The person who was Alice 5 seconds ago is now Bob with neither warning nor notice. From the system's perspective, Bob grabbed control of the body and won and is now fronting.
Schizophrenia
ElijahRyne has a really good basis, and honestly I'm just going to use that, but maybe refine it into this:
You can enforce your views of reality on others. In effect making them see what you see. If I had to go from scratch, I'd probably do something like being able to focus more easily on your Powers because you're always in your own internal world, so any abilities that require you to meditate or concentrate you just meet those requirements for free. But I like the idea of bringing other people into your world. It doesn't produce any external effects, just as Schizophrenia is not linked to external reality, but it has an impact and a presence, and maybe they don't even know they can do that.
Further Notes: You want to think long and hard about how you want your Powers to work when the Illness is being treated. If the Illness provides the Power, then it makes sense that treating/"weakening" the Illness will similarly weaken the patient's Powers. This however provides a disincentive to seeking therapy/treatment, and you want to handle that with extreme care. It's not impossible though: I actually do something like this. I have written that if you're trans and a spellcaster, you can transition, or you can keep your spellcasting, but not both (Edit to add: You can perform modifications to your body at a tech level far below our own if you want to transition and remain a caster, but then you face those complications. So it's really a Transition / Spellcasting / Bodily Health, pick any two). If you're not a spellcaster, then transitioning is still there, and a very strong option at that. An alternate way is that the Illness predisposes you to acquiring certain Powers, or awakens those Powers, which you then get to keep or even refine/make stronger as you persue treatment. This opens the door for people without Illnesses having Powers corresponding to Illnesses, but it provides a very strong "know thyself" theme that a lot of people would find wholesome (If you want an example of that done right, I hear the video game Celeste is really good at it.)
Also again I stress the importance of actually talking to varied people and getting a more holistic view of the world. Research on something like how humans grok will never be accurate: humans change with time. You want to make sure you have a solid foundation of core experience underneath and supporting any research you do.
You are undergoing a very difficult challenge, and honestly? If you really stretch yourself, you just might make it work. But you need to make sure you know what you're doing. Because this IS a challenge. No one will fault you if you step down.