Probably not, no. The countries with similar climates have an obvious advantage. It may not be as much of a problem in Qatar as people are expecting though, as wasn't there some talk about playing all the games at night?
Sturridge isn't overhyped, he isn't really hyped at all. What he does have is a better record both up front and on the wing than anyone at Liverpool other than Suarez, and by rights should be Chelsea's first team striker really.
No he couldn't. Mourinho doesn't make even twice as much as him, let alone five times as much. Wenger is the fourth highest paid manager in the world and hasn't won anything in years. He has a seriously cushy deal, perhaps more so than any manager.