Perms basically allow you to attack, in one way or another, the person you have perms on. What you can and can't do with different types of perms can be read about
here. Often times it's very situation specific if someone has perms or not, but if you physically attack someone or threaten to physically attack someone, chances are they get perms on you from that. Best course of action would be to ask a staff member - show them screenshots of a fight or situation you've had with someone and ask what kind of perms they might have based on that. If someone claims to have perms on you, it's also best to get a staff member to verify if the perms are valid or not.
All perms last a real life week, and the person who's the target of those perms needs to be online for at least one real life hour every day while those perms are valid. Using any perms needs a valid motive, and "I want to attack them because I can" isn't a valid motive. You can ask about the validity of your motive from a staff member as well.
What you can do without perms varies too, and you sort of still need a motive to do anything even without perms. It's still very much situation specific. Different staff members might also give conflicting information on what you can or can't do. I've heard you can pick people up and carry them without perms, you can unmask someone without perms, you can initiate a fight without perms (but not knock them out unless they fight back), among others. My advice would still be to ask staff if you're unsure.