I'm trying to beat Chapter 2 at the moment - it's not easy, by the way...
Yep, solo chapter 2 is definitely a doozy--from personal experience and reading other threads, expect to lose a dozen or so times before victory!
Tony Merz is in the deck I'm drawing cards from. If I understand it correctly, I can only get this card into my hand only if I draw it in the beginning of the round? So if Tony Merz or any other character is drawn during Phase 2 or Phase 3, they are just discarded?
Correct on all accounts, although there is an event(s?) that lets you draw cards outside of the first phase, so you might draw him then as well.
Also, the small watchtowers are in the deck right now, but is Rabbit supposed to be in the deck during chapter two?
Yep, Rabbit gets added at the end of chapter 1. Very good luck to you!