I think it'd be cool, but the only problem with that is, everyone knows about the Master Sword in OoT, and how Link pulls it... but where's Fi? Although she may not know this is a relative of Link, this is highly unlikely. I'd love to see Fi in another game, but it's highly unlikely that she'll appear, for at least a while. But I also agree with Impa's statement, she could have been referring to the sword rather than herself. But still a good theory, I'd love to see her again.
No. At the end, Fi says she will go into an eternal sleep within the Master Sword. "May we meet in another life" is most likely a refrence to how Link's descendants, aka the other Links, use the master sword in other games later in the timeline
I think Fi may be reincarnated into one of Link's helpers in the other Zelda games. Or it may be referring to when Link gets the Master Sword in other Zelda games, they are meeting again, but Fi just doesn't talk.