Is enclosing external wiring in conduit standard practice? Is it a code violation? Since I'm HVAC ignorant, will my HVAC contarctor be offended by this request?
Any time Romex is exposed and not encased within a wall is against code. It is not designed, with the exception of an attic or run within a protective chase, to be left exposed.
If your contractor takes offense to your insisting upon a quality install, you got a problem. What's this contractor going to do if something goes wrong later on down the road with the system?
I would not tell your contractor where you got your list of corrections of his work, but I would insist without wavering that everything you find disturbing about this installation be corrected before you settle on the bill.
Psychrometrics: the very foundation of HVAC. A comfort troubleshooter's best friend.