Just my $0.02 ... I've never used Dawn on anything prior to using Glare, with no ill effects that I'm aware of.

Do the Glare instructions say to do that somewhere? I'd be very hesitant to use anything that's not an automotive or motorcycle-type washing detergent, but that's just me. Also, I've never noticed temperatures having any effect one way or the other, but you do need to let the product dry completely. I'll normally let it on there an hour, just to be sure.
As far as all the products you bought, start with the least aggressive (the Pro Polish) and see what results you get, first, then go to the next aggressive (Spider) only if you're not happy. I'd be very, very surprised ..... no, shocked and dumbfounded, actually ... if you find you need anything more than Spider on a 2011.
I agree with Sypder, the polish should take out any leftover bug remanents on the paint as you're applying it. But, be very careful about not getting the Pro Polish on any rubber or plasic parts. Chances are pretty good you will not get if off if you do. The secret to a good detailing is making it look like it's never really been touched/waxed before.