QIf I reveal a Trigger with a drive check, can I resolve this follower's "Whenever a follower on your field performs a drive check" ability before I resolve the revealed Trigger?

ANo. You have to resolve any revealed Triggers first.

QIf I play a follower's Twin Drive ability, does this follower's "Whenever a follower on your field performs a drive check" ability trigger twice?

AYes. When you play a follower's Twin Drive ability, it performs 2 drive checks, which will each trigger this follower's "Whenever a follower on your field performs a drive check" ability. However, you have to resolve both drive checks before resolving this follower's ability.