QIf I play this follower's Fanfare ability while Overflow is active for me and my opponent has 2 copies of Vania, Kind Queen on their field, do any Forest Bats they play during their next turn cost 0?

AYes, that's correct. The total cost reduction would be -1.

QIf I play this follower's Fanfare ability while Overflow is active for me and my opponent banishes 10 spells from their cemetery to play Dimension Shift during their next turn for 7 play points, does it instead cost 8 play points?

AYes, it does.

QIf I play this follower's Fanfare ability while Overflow is active for me and my opponent plays Merlin's On Evolve ability during their next turn, does the spell they play still cost 1 more?

AYes, it does.

QIf this follower leaves the field after I play its Fanfare ability while Overflow is active for me, do cards my opponents play still cost 1 more during their next turns?

AYes, they do.

QIf I play this follower's Fanfare ability 2 times while Overflow is active for me, do cards my opponents play cost 2 more during their next turns?

AYes, they do.