He didn't have a name, nor a job, but he had an apartment?

I know that there are a lot of weird things in this movie, and I don't know if this bothered me per se, it's not THAT important, but if I made a movie, I would be laughed out of the room by my friends if I set this up, without it being explained. It just doesn't feel very serious. And don't give me "this is fantasy, because fantasy just means that there's a special set of rules for this world. And those rules are for an example that "guardian angel"-horses can fly, and that demons exist, but the rest of it (that isn't also clearly stated as supernatural or going by special rules) is supposed to follow reality. And nowhere in the movie is it stated that you don't need money to live. Peter even steals to get by in the "past" and he also pays the stable guy, so clearly you need something of value to pay for your things, such as clothes and an apartment. Both of Which he just miraculously has in 2014, without even knowing who he is or seemingly having any kind of employment. Also, don't you by law? Have to show identification and put your name on the lease, when buying and apartment? And he doesn't seem like the type to lie.