Both can be correct depending on the context. An armchair has arms. A person sits in an armchair. [inside the space defined by the seat and the arms] An ordinary chair does not have arms. A person sits on a chair. [on the seat of the chair].

Depends on context Gold. I would change "the" to "his". Examples: A) We worked on this project for 15 hours yesterday, and where was Joe in all this? He sat in his chair like nothing special was going on. B) After being scolded by his grandmother, Marco did the right thing and sat on his chair. Tom

He sat on the chair