Everyone felt like that. He didn't choose Red specifically out of the bunch. Infact, he would have chose Cloud over anyone.
The fact that neither Cloud nor Sephiroth touched the top of Shinra Tower, where it collapsed, disproves your theory, as well as nothing else was falling apart before Cloud and Sephiroth began fighting. Infact, the only part where anything fell apart was when Sephiroth brought down the tower.
No, it isn't. A game-mechanic would be like in the flashback, Sephiroth can't be damaged at all. When Sephiroth displays an immunity to a spell, it's not a mechanic.