I would not mix your micro fiber towels, app, etc with cotton towels. Just wash them separate. I would not use Dawn. Just use a nice laundry soap without fabric softners additives like Tide. I also tend to put some vinegar in the final rinse.
Personally I wash sheepskin mitts by themselves, and I wash MF towels and applicators by themselves. I wash foam applicators in with cotton towels.
I always use hot water, and like everyone else, I just use a good laundry soap. I prefer one without dyes or scents. I will also use vinegar in a Downy ball to help any soap residue rinse clean.
If you don't have enough for a full wash, buy some more.