1. Should a Barrage timer be implemented?
No. Never liked the idea of knowing exactly when you'll be unfrozen, a timer definitely detracts from the skill of nh/bridding.
2. Should a vengeance timer be implemented?
Don't see why not, any skill using vengeance has always been timing it correctly - not spamming it when its cooldown is almost finished. It does already get greyed out when it's on cooldown, so it's not too big a deal either way.
3. Should various potion timers be implemented? (Stamina, Anti-Venom, etc)
Again, don't see why not; it's just a QoL thing, ultimately.
4. Should the timers be automatically turned off at ::brid/::edgepvp?
Yes. OSRS switches are already forced there, so it makes sense to disable timers there, also.
Oh, and, if they are added, they should also be disabled in tournaments.