1. Does it need 50 wins to make the playoffs in the West?
No. It'd probably take 42-46, but not 50. I'd probably just insert the Lakers at 4 and push everyone back one, which would mean the Grizzlies and Nuggets fighting it out for the 8th slot. It'd probably take 44/5 wins.
2. How do you rank Lakers in the West?
Probably 4. It would depend a lot on their supporting cast. But given the Lakers usual regular season slumber during their most recent championship era, I don't see them having a better record then the Suns, and that takes them out of the top 3. (The top 3 seeds go to division leaders, and they're ranked accordingly.)
3. West 8th seed will win more games than east 1st seed?
No. Didn't the Pistons teach us last year to stop disrespecting the East, especially against an 8th seed? If anything, the East's top seed might have more wins then the West seed, with the Heat not being championship contenders, and some of the moves made to counter them not being made.
Assuming Lakers did not trade Shaq and Shaq got along well with Kobe.
Well, them getting along has little to nothing to do with them oncourt. They won 3 championships, and they weren't the best of friends then. They're both good enough players to leave offcourt issues offcourt.