#3
Yeah, i think Epi might have made the Gothic Les Paul with a Floyd Rose on it once, but its discontinued now. I know they definately mdae a gothic Explorer with a FR on it, but that's not what you're asking. Yes, it's very possible, but you'd need to do some routing, and you'd have to fill in the holes left by the existing tune-o-matic bridge, hence requiring a refinish/partial refinish as well. It would be a pretty tough job, but possible if you have the tools, skills and patience.
My gear;

Custom HSS Strat (eBay'ed parts)
Fender Acoustic
DOD EQ
EH Big Muff
Home-made Wah
Home-made Booster
Laney LC15

Looking for a Jazz Bass body to refinish

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#4
yes but loads of routing and if you stuff up you could waste your guitar. also you need to take out parts of your fretboard to fit the nut