Hey there, I live in the place so here ya go.
1. USUALLY I don't experience mosquitoes/noseeums in Zion. Not a lot of standing water and noseeums seem to enjoy lower elevations. Take a bit of deet, no need for headnet.
2.Just flew over Zion in a plane the other day (lucky me), most the traverse is damn near hike-able now. Not a lot of snow at all. Of course this will change a few times (like this weekend) as we get a few more snow storms. The snow will melt fast (temps have been up to the 70's already). Hopefully not too many cold storms hit between now and your hike.