"Am I to old?"
Nah, you still have alot of time left before you're too old to learn.
"And what to do? I don't have much money, so I can't just buy cars, crash them and buy new ones..."
No one does that. They take old cars, sometimes crash them and learn that way. You'll find that even the pros, in the beginning of their careers don't use "new" cars. They find old cars that resemble their flagship vehicle in performance and practice with them instead.
"Do you know if I can just go to some school and get a car? Or do I need to have my car..."
Unfortunately, your part of the world doesn't encourage rallying or most motorsports like western Europe does, so it'll be hard to find a school. It would be good if you could find atleast an instructor who can guide you through the basics of rallying. But, if you can find a school, in about 95% of cases they will provide you with a car. You will have to put an insurance deposit and pay a part of the damage if you total the car.
Rallying is a rather simple sport to learn. That is why I personally favor it over any of the other motorsports. It's simple because it's realistic. You take a normal, stock car, go to a normal everyday road and race. Of course, the pros modify the cars, but you can still learn a lot on stock cars if you're a beginner.
So, find an instructor, get a cheap car that you won't have to worry too much about crashing, get the safety gear, find a race track/road, and get started from there. Even if you don't make it to the pros, it's still a great, fun sport to take part in.
Former Pro-Rally Racer
Former Street Racer