Mosquitoes will be there in some quantity - they have been present in some degree pretty consistently everywhere for the past few weeks, from reports and my own observation. It's a late spring.
http://forecast.weather.gov/MapClick.php?lat=37.74384267225534&lon=-119.58154678344727&site=hnx&unit=0&lg=en&FcstType=text is the Yosemite valley forecast - ignore the Mt Whitney on the map, it's not there. Clearly they are borrowing info from Google, which also thinks Whitney is in Yosemite, they are wrong.... The weather forecast is prone to being somewhat different than predicted, but it is what it is.
There is probably melting snow above 9,000 - 10,000 feet. Things were really starting to thaw a few weeks ago and I don't doubt that's been helped by the rainstorms that blow up in the afternoons up there. However, you can have light snow any time in the high country including midsummer, so don't go unprepared - take at least a poncho and an extra layer or two.
Red Peak Pass likely has snow on the north side - check with rangers, they frequently get reports from other backpackers.