Will a wool pad work with a DA polisher?
Yes, a Purple Foamed wool pad will work with a DA. However, I would suggest looking into the Surbuf pad line. These pads use very short "microfingers" that efficiently transfer the power. A traditional wool pad has very long strands that will waste the DA's orbital pattern.
What size backing plate should I use?
It all depends on which size pad you go with. With a Surbuf pad, you can still use a larger sized pad and plate.
Should I upgrade to a rotary or stick with more advanced pads?
I would stick with the more advanced pads. There have been many significant improvements in polish and pad technologies that make the DA much more capable. I foresee the DA getting even more capable.
On the flip side, rotary polishers are always fun to have around. For the first pass on a wrecked finish, they work great.
Why don't they make a machine that can change between a DA and a rotary?
Dynabrade makes an attachment that converts a rotary to a DA.
Should I upgrade to a Flex DA?
Maybe, but it's up to you. I have used a Flex before (rotary and DA). The rotary is fine, but I really dislike the rotation of the Flex DA. Maybe it is because I am used to working with a clockwise rotating rotary, but it seems like I am fighting it. However, it is a very capable machine. That being said, I can take my beater 7336 with a Surbuf pad and some M105 and hammer out 1500 grit sanding marks all day.