Turns out the cat I got doesn't know how properly clean himself and he stinks quite a bit. Plus he seems to have been used to sleeping on people's beds so making him unlearn these habits (first he switched to sleeping in the litter D: ) in his new home turned out to be a full time job. But luckily I have fixed most issues within the last 3 days so I can start spending more time on other stuff. I also taught him to play with some toys. Luckily that takes maybe 15-30 minutes per toy.
I still have to make him unlearn that I am not a toy (he climbs all over me, lol), to stop licking my face (apparently just blowing some air into his nose works wonders and I was amazed how well it works), to clean himself better and that he fully understands where his actual sleeping place is. He still tries to climb the bed all the time, but at least he goes to his actual sleeping place when I lock him out of the room. And yeah, he still stinks (along with his pooh which stinks horribly). I hope that after he can clean himself properly and after he gets used to his diet, it will go away.
I also have to pay the vet a visit to have him checked. The stinky pooh could be a disease or worms (not just the sudden change in his diet) and I have to get him sterilized anyway. At least cats are incredibly fast learners. You just have to give it all a couple of hours across a few days and a lot of patience. Seriously, he's been eating away my nerves so badly that I didn't eat properly the last few days. And I am a very, very patient person. D:
EDIT: I think that he thinks I'm his mother, though. When I lock him out of the room, he starts meowing like crazy and when I open the room, he runs to me and starts brush himself at me and all that stuff as if he's totally happy to see me again. xD In the first night I let him spend the first half of the night in my bed, but after 4 really bad hours of sleep, I realized it's not going to work this way. He was playing with me, scratching me and biting me almost the whole time I was asleep. I felt the scratches and bites in my dreams quite a lot. D: