I for one think it would make an interesting storyline with the "Thomas Riker" Barbarian having a rivalry with his "younger twin brother."
I haven't seen you before...
I was saving the Empire from evil while you were still in short pants, junior
We're both still wearing short pants, 'old man.'
Hey, toss me that sword, I might show you how to use it
Anytime, I'd like to see you try to keep up!
The elixir doesn't duplicate equipment. Heroes can't kill each other (except perhaps in the case where one of them has gone under the influence of "Command").
So no "infinite gold by team killing and looting the body" loophole in the NA rules anyway.
Would a revived wizard get all of his spells back? I don't think so. I would say if he cast those spells while alive they are used up until the next quest (based on a device, not an inborn ability... if anything his magic is just his aptitude in interpreting the magic books or whatever to get them to do what he wants until they need recharging).
Yes, I would agree that if a starting Barbarian died, and monsters stole his loot, he'd come back alive without armor and just his bare hands (1 CD) to fight with, not magically also spawn a broadsword. If it happens between quests, he doesn't get bonus equipment, he gets whatever the other heroes give him or uses the gold they gave him to buy more stuff.
The Elixir of Life is a chance to revive a dead hero. The normal process is that you make a new character. That means a new Barbarian comes in with a new name but otherwise he's identical to the old barbarian you once controlled, albeit with his starting gear only. Yes, I see it being used more like in the same quest, shortly after the guy died, as opposed to reviving a hero that died 15 quests ago. Would there be two barbarians then?
The game was originally built for 4 heroes. So in theory you could have more, but later packs say you can only have one of each character type in a quest at a time (not counting NPCs) so you would pick which barbarian went on which quest. It matters little unless you want to split up the gear and give some to each (I guess for safety, since some of it could be lost forever to monsters, except Artifacts which theoretically Zargon brings back early in the next quest as a special treasure). It may seem like a cheat, but players get attached to their heroes and want the satisfaction of knowing Zargon didn't kill them... at least not forever. That's how I see it anyway. If one doesn't like the Elixir of Life, there's always the EU ruleset which only uses it once (in Dark Company) and it functions very differently there only bringing the hero back with 1 BP.
Maybe you could get around the "twin brother" issue by saying he revives at home or something (so you can pick him up when the next quest starts). Or, yipee kye aye... suddenly there are two Barbarians (and at least one of you will control him plus your other character or characters). Pretty awesome! But you can't purposely kill a hero, hope you find the Elixir, then use it to revive him so you for a short time have double character tornado tag team action at summer slam brother!!!

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(*then again, if it's about fun and coolness above all, if Zargon says it's okay, why the heck not...)