Ok, before anyone who doesn't know what their talking about starts to quote the BradyGames strategy guide like it's the all knowing truth replies, allow me.

1. Yes, you can kill it in the first battle.
2. Just keep attacking, don't let up. I think it has to go down like 5 or 6 times before it blows up.
3. Not if you see it blow up. If it just goes down and you run, then yes it will keep chasing you. But if it blows up, then no. The battle music will also stop playing when it blows up.

I say this having actually done it myself. Zell will tell you that you should run after it goes down the first time, but you don't have to run.