Will a 6' ultralight be able to run these okay, or will I need a light action?

You should be fine, I used the "0" and "1's" with an ultralight for trout for years with no problems. Since then I've switched to Panther Martins though, the blades turn much easier on a slower return.

TMF, an ultralight will run them just fine, but if you are going to be purchasing a new rod already, I would look at a 6' Light action, better hooksetting, better casting, and usually more sensetive. Just my opinion.

Depends on the rod itself, some are more noodles than others; simply some flex with very little backbone to them. Everyone has a different feel for fishing, so...It might be worth the experience to test both ultralight and light for oneself to gauge the difference.

UL action will be perfect. I run the 0's with an UL rod and its great for pannies and smallmouth.