The correct answers are We discovered fifty critical bugs, most of which were caused by the recent update. and I spoke directly to the senior engineers, several of whom denied any responsibility.

When combining quantifiers (like most, several, all, none) with a preposition (usually of) in a relative clause, you must use which for things and whom for people.

"Most of that" and "several of who" are incorrect.

Additionally, "most of which they were caused" is incorrect because "which" already acts as the subject of the relative clause; adding "they" creates a double subject!