Can you see Avignon and Arles and the Roman aqueduct in 2 days
Certainly. Stay in Avignon, and do daytrips to Nimes (Pont du Gard) and Arles.
You could - but it would be very rushed.
I would stay in Avignon.
You can take the train to Arles and see the main sites there in 3/4 of a day, then go back and spend the late afternoon and evening in Avignon.
The next day I would go to the Pont du Gard by car which could be done in a half day, then go back to Avignon and see a few things there.
Yes. No problem.
Yes you can, I have done this but I wish I had had more time. Still, it's all worth it!
My own opinion is to avoid staying in Avignon, or at least in the old town, at all costs. Taxis can't go there. And frankly, the entire city falls way short of charm IMO.