Hello, I want to buy bitcoin, how can I be sure that they were not used for any shady business? If I buy directly from a person, what is the chance that I will have problems later? Do I only have to buy from exchanges?
You will not have problems later. If you have any problems, they will be immediately.
Buying through exchanges is usually a lot safer, as some exchanges trade millions and millions of dollars everyday, so they are not going to steal your money. However, unless you know who the person you want to buy your bitcoin is, it is like a shot in the dark (you can get scammed or not).
If you buy from exchanges, immediately move your bitcoin to your personal wallet. I recommend Electrum, from electrum.org