Are we allowed to have our phones at SW Prep and A&S to FaceTime family on the weekend?
You will have access to your phone through some points in Basic and when you are at SW prep/A&S. You will also have most weekends off while you are training.
After basic training, when will I be able to normally use my phone to video chat with my family and friends?
You will be able to have your phone at some points even through basic, but you will always have it after duty hours at selection. You will have an opportunity to spend time with your family after you graduate basic. But you need to get your mind right, YES talking with family is very important, however you need to not worry about that. Focus on passing and getting through.