4. The search committee goes through a lot of work to coordinate your interview. A note to the chair thanking them for how smoothly it ran (rather than simply for the invitation) or making you feel welcome is probably fine. If a member other than the chair did the arrangements for your interview, I'd send the note to that person instead of the chair.
I am pretty much with Copper, especially on the bolded points above.
My take on it? Email the SC Chair, ask her/him to convey your appreciation to the rest of the SC and the department. Email the administrative assistant and thank her/him, because her/his efforts are probably primarily responsible for making your visit go smoothly.