Are you wanting guidance to ask these questions to a potential candidate or brain dump them so you can manipulate yourself into a role which may well be beyond your skillset?

Quorum is not an object, it's a state in the cluster that exists and must exist for the cluster to maintain availability.

Witnesses are objects, and I think this is what you were referring too, they take the form of a disk object or a remote fileshare object. However, with the right cluster design neither of these are required to maintain Quorum.