Will they grow in partial shade? Will they survive winter in a flower pot?

Shasta daisies are meant for full sun. They may grow in partial sun, but they will not be as strong as they would be in their full sun habit. You may end up with shorter, thinner plants that seem to limp along.

You can pot them up but they will still go dormant. It's best to cut them back after first frost and they'll come back in spring. If they are in the pot now, cut them back after first frost then put them in an unheated garage, basement, etc. If you have them in a pot already outside and the pot is too large to bring inside, just cut them back and they'll come back in spring

Please let us know your location,it will help to answer your questions
I see you got your answers while I was typing lol

Christine is right though. We do need you to fill out your profile with where you live and what your zone is. Alot of times that alone is enough information for us to help you off the cuff.

Hi YorkieMom
I'm in zone 4b and my daisies do great in a whiskey half barrel. They go dormant in late fall, stay outside all winter and come back with gusto in spring. The more sun the better/fuller the bloom.