I'm not entirely sure on them all but it appears to be situational. In the book of Job Satan is first allowed to harm Job's family but not Job himself and then allowed to afflict Job with a skin condition which seems to be a way to test his faith, have a read for yourself. The first two chapters (pages pretty much) show God's relationship with Satan with the middle showing Job coping with the issues and discussing them with friends and there's even questionably a description of a dinosaur (the behemoth) in there.

From observation I think that Satan's restrictions are related to how he is trying to manipulate such as organizations marking themselves with logos. The serpent on a stick for example which we see all over the place from the WHO to barber's poles which relates back to a story in the bible where the Jews are rejecting God's gift of bread (Jesus, Manna) and they are attacked by serpents and God tells Moses to offer them an alternate savior from their afflictions in the form of a serpent on a stick.

It's super strange when you think about it, the biggest "christian" organization in the world's leader has an audience hall shaped like a serpent's head ( just search images for pope snake building). Then those who actually title themselves as "satanists" are allegedly really atheists who are mainly interested in making a mockery of Catholicism. Everything is some sort of backwards in this world, it's as if Satan doesn't necessarily have to trick you into doing the wrong things as long as he keeps you from doing the right things.