I got caught by an inspector for not having a ticket on a tram. What powers do they have? Can they arrest you?

No, these inspectors (revizoři) are not allowed to use force to hold or detain you. They may, however, call the police if you refuse to cooperate. Of course, at the same time, you are legally required to show them your ticket or proof of your identity even though they have no legal means to compel you to do so.