Replying to Beartooth Highway Summer Backcountry?

Hey guys, I am going to be driving cross country this summer from Marquette Michigan to Mt. Hood, I am making the drive somewhat of a road trip and the route I am planning on driving goes over Beartooth and Teton Pass.

My questions are, how is the snow pack this year? Will both of these passes likely be open this year by Memorial time?

Is there any road lap style back country access on either of these two passes that will still be skiable in the late May/Early June time frame? Anything with short approaches? I will have an AT setup with me.

Is there any good free camping along back roads in the Beartooth Pass area specifically? Looking for a spot to basically park my car off a two track somewhere and just sleep for the night so I can continue the trip.

Also if anyone is interested on splitting gas for a one way ride to Hood let me know, I should have some room!