Has there been a precedent for these things in the TES world? There are haunted locations, which are places ghosts happen to hang out, but what about exorcism of spirits in a place/person? Can spirits forcefully enter the body/mind of the living?

Well we know Daedra can possess a person's body because of a quest in Daggerfall as for hauntings those have been in numerous games such as Morrowind and Oblivion. As for exorcisms there are probably ones for Daedra and supernatural possessions but they never really went in depth with that.

Hmm. I suppose the 'Banish' weapon feature might be considered exorcism, but it concerns daedra rather than spirits. And I can't imagine priests of Arkay hitting innocent people with swords and axes.

Theres also banish daedra spells.

When you summon a daedra, your mind is linked to its and its mind is linked to yours. It's a constant fight for control, which is why a skilled conjurer needs a high willpower. Would that be an avenue for possession?

I like to think that lycanthropy is a type of daedric possession. There is at least a wolf spirit that inhabits your body, as the cure in Skyrim involves separating it from yourself and killing it. It could be assumed the spirit is one of Hircine's pets.