This is Horse Shoe Meadow. I have never not found a space to park or camp. I've been there many times and one time was the only one there (late season).
I have always paid the fees, but I don't think anyone checks. You put a hanger on your rear view mirror from the registration.
If you are a through-hiker and not camping then the parking is free.
Don't expect any cell phone coverage there. Also, have at least a quarter tank of gas before heading up if you are driving.
You have to camp in designated areas. We were warned about this.