System design is not a typical part of a research interview.

Yes, they do. The rule of thumb is: The higher the level you are hired, the more wiggle room is there. A random PhD grad will need to pass the normal coding screens which are carried out by SWEs who do not know anything about the candidate.

Last q depends on the FAANG org, everything exists. MS research is very pure, Amazon/Apple very applied, everything in between.