I plan to use my old laptop ThinkPad R500 as a server.
would that work? Or would the laptop break down very quickly or could it become dangerous, e.g. That the laptop starts burning?
The laptop comes from a company and was there occasionally every day around the clock.
A normal PC let alone a laptop is intended for server use but would break very fast probably not. You can always have bad luck but usually keep it a bit. And in terms of burning: CPUs (the component that's usually hottest on normal PCs) have a power-down protection feature that cools down the CPU until the performance gets too low and the PC / laptop just goes out. That's why theoretically nothing can go wrong, and there can always be mistakes, which are extremely rare.