I can answer your first questions but not your second one
I send thank you emails to all faculty I interviewed with and program leadership. Not sure if by letters you meant email or actual letters, but I tend to opt for email over sending t/y notes via snail mail because of timing and most faculty are still working from home. I keep my email brief, but usually try to personalize it.
I also think it’s good practice to send thank you emails to all administrators/admin assistants and student hosts - even if they are not involved in the actual admissions decision, they still put a huge amount of time/effort into this process!