Deffo no way.
It's as the card/effect text says - "reduce COMBAT LEADER's combat value..." so not the support gang. Not only would that be thematically weird, it'd make the game unfairly difficult!
(rather than being rewardingly difficult, hah!)
Remember that you get to go first on Tactical phase, so you can mitigate/reduce impact of any venom support cards that hammer your combat leader, if you want. Me..., I sometimes 'sacrifice' the combat leader and let the Venom cards batter him, choosing to offset bad cards that impact some of the support vehicles or troop cards I've got instead - as they will do the damage instead. I see it as the combat leader 'taking one for the team'. Man, I love this game!
Correct, if you have no dice left then you no longer pull any from the leader. That is why you lay our dice out on the cards providing them so when you start pulling you know where they pull from.