We love this area. You get your permits at the Summit Ranger station. They are free, and there are no trail quotas. You will have to tell the rangers where you are going to spend each night---or they will tell you. We often vary from this route once we have the permit, but you need to know it is part of the process.
Anything we would post about mosquitoes right now would be out of date in a week. Snow levels are about 9,000 right now. We were at 7,900 feet on Friday, and the only snow we saw was on a very steep north slope at that elevation. But at 3 p.m. it was 47 degrees, and blowing about 30 mph--absolutely freezing. We've had snow in June at 5,000 in this area...so expect the weather to be unpredictable.
Stream crossings may be something else. Last I saw, both Piute and Cherry Creeks were running very high, and considered uncrossable right now. That's not a joke. EMigrant is a huge granite bowl, and when the snow melts, all the water comes down that granite like a giant flushing toilet bowl. Don't get hurt.
WE've got a full trip report on exactly the trip you are considering on our website at backpackthesierra. com. The granite between Pingree and Big Lake is simply unbelievable!