Hello! I’m one of the handful of alolan trainers lucky enough to have recieve a rotomdex. The little guy’s a sweetheart, and super helpful too. Recently though, he ended up getting sick. I took him to the pokemon center near my house already, and they looked at him and gave me some medicine to relieve the symptoms. Thing is, he wants to stay in the ‘dex while he’s resting. He says he’d prefer being able to talk to me normally, and he feels more comfortable that way. (1/2)

To him, no, as your rotom itself is technically in an incorporeal, electric state. If anything, this may be worrisome because the medication is only effective when rotom has a body—that is, when it’s not possessing something else. For this reason, his recovery may be slow going, although if you regularly coax him out to take his medicine and rest for a few moments, he should eventually recover.

To his chassis, possibly. When a rotom overheats while possessing an appliance, what’s actually happening (other than literal overheating) is that rotom is generating excess electricity. This risks overloading its borrowed body, if the heat doesn’t simply melt the wiring.

In short, as comfortable as he may be, he really should spend time outside of the pokédex until he’s feeling better.

As for your second set of questions, from what I understand, it’s more that Kukui selects rotom he’s befriended and deemed responsible enough to take care of his proteges. This may sound a little odd, but from what I also understand, this is completely typical for Professor Kukui…