How Cloud could throw Sephiroth into the Lifestream and all that? I guess that was just a pure adrenaline rush or something
It was AFTER that which Hojo came, gathered up all the survivors, including Cloud and Zack, and performed experiments on them. Tifa on the other hand escaped that thanks to Zangan (you can find this out by reading a letter from Zangan to Tifa found in Tifa's room, in her piano if you play the right music on the 2nd/3rd disc IIRC). Before the whole Nibelheim incident, Cloud was just a regular guy (except that he may have been showered with Mako like all SOLDIER members when attempting to join SOLDIER).
EDIT: I'll just add that the game doesn't explain how Cloud survived the attack and managed to throw Sephiroth in the the Lifestream, but fact remains he hadn't been "enhanced" through experiments yet. What I'm guessing is just that the stab is not as bad as it looks, maybe it just cuts through the side of his uniform under his armpit or something, and in an rush of adrenaline, Cloud grabs the sword and tosses Sephiroth down into the Lifestream. There can be other explanations as well, but this seems fairly believable to me