I think the only way he really has a chance to lose in New Hampshire because of a loss in Iowa is if Christie does much better than expected in the Iowa caucus. Cruz is going nowhere in NH and any post-IA momentum for him is only really going to affect the SC primary.
I doubt he loses it. It depends what happens in the next month but Iowa is really useless on the Republican side. It hasn't picked a nominee correctly since 2000.
Well, that just means it only failed two times in 2008 and 2012 (barely). Two in a row does not a pattern make.
It voted for Bush in 1980, and Dole in 1988. The only times Iowa has really picked the winner is in non-competitive primaries like 1992, and 2000. Dole also won it in 1996, but I'm not sure if you'd call 1996 a competitive primary year.