I think the answer to number 1 is no, not in any meaningful way. At least the way they wrote this season. The things Szilla and others are trying to give it credit for I feel other factors actually were the real driving force behind, and I believe its obvious Varys would "betray" or turn away from Dany regardless of Jon's parentage as soon as she showed her "Mad Queen" side. Not that Varys' death meant anything even when it happened, because he didn't do anything meaningful this season besides send out letters no one apparently received, or try to poison Dany unsuccessfully (if you buy into that theory). He told both Jon and Tyrion what was going to happen with Dany before it happened and neither did anything anyways until after it happened. It's pretty sad actually that Varys could have been removed entirely from this season and nothing would have changed whatsoever.
Yeah, to be honest, I shouldn't have said meaningful. It had some impact on the narrative but was really a means to an end - getting Daenerys to snap. When in reality Jon's identity and his parentage were issues he grappled with his entire life, but this had virtually no impact on his character or story arc