Q1: No, it does not require X. But some software even if not graphical, requires X libs for whatever reason (e.g. Using Qt)
Edit: to answer Q2: I don't think there is technically a way to interact with the system without a TTY but thats technicalities. Your more practical answer is to use SSH to log in and interact. This is how most IoT things work which run Linux and have no display capability at all.
Use
screen
?Maybe I don't understand what you're after. But 99.9% of Linux systems don't use X. But none of those are desktop PC's.