1) Sephiroth was acting on his own will (confirmed in square ultimania guides), however, in the end he was carrying out the will of Jenova, even if it was to make himself a god.

2) I don't think so, although Tifa called him 'cold' and he decided to not search for the missing Shinra soldier that fell during the bridge collapse

3) He seemed real reserved and stoic, yet arrogant after his emergence of consciousness from the lifestream. You didn't get to see alot of his personality throughout the entire game, kinda like older FF Villains such as Garland, Palamecia, Xande, Zemus.

4) I guess i can explain it - it's The Jenova Reunion Theory. Hojo explains it on the Highwind ride with Shinra's high-ups to the northern crater, and explains the rest of it while there. He hints at it if you talk to him at Costa del Sol when you first get there on disc1:

If you separate Jenova into pieces, eventually the pieces will join back together. That's why the event was called The Reunion. Hojo does say he thought the clones would head to Midgar, where Jenova was located, but instead they went to Sephiroth. Although, this is what happens:

Zack and Cloud were travelling to Midgar just before the start of the game. The man in the tube in sector 5 (aeris' town) also showed up on the outside of Midgar. And of course, "1", the sephiroth clone you follow throughout the game also went there, to retrive Jenova. So I think they go to meet Jenova, as opposed to Sephiroth, until "1" took the body to the northern crater, where all of them except Cloud died.