You and I are cut from the sme cloth, it seems. My own personal recommendation is... Stick with this job because there is a huge opportunity for you here. This is why I see it - you said they're disorganized and value highly trained people. There is no central place for data. My recommendation would be to take advantage of the fact that you're training to start laying the seeds for organizing information. Type up notes or something. At the very least, it gives you something to focus on other than the stupid things depression makes you think about. It can also make you look like a go-to person when as you said, ask a different person and get a different answer.

I think the desire to want to sneak away is the depression talking. I am at about the same point. I've been at my current company for 6 months and last month they offered be a full time position. Great pay and benefits, wonderful, but the environment is gossipy, people are lazy, and no one friggin shares information (even when they are supposed to). I start feeling like this place is awful and I remember that every company is going to have their own problems. You're going to have bickering in close quarters, so just wear headphones.

I get you about the feeling like all you do is work and sleep. I felt like that way for a while but its because adjusting to the new job was draining and made me tired. I'm slowly rebounding and working out a more ideal schedule so that I feel like I get a little more out of each day.

It's a process, but you got it. You said yourself they like the work you do, so keep being awesome and don't worry too much. it'll get easier with time as you find your own way to adapt.