Hello and welcome to YT! May I suggest you ask all your question in one post instead of posting new threads? I think it'll be easier to follow.
If you haven't already, a good place for new parents to start is here:
http://www.yorkietalk.com/forums/gen...w-parents.html
I believe you shouldn't take them out until the puppy has all her shots. But I think you're supposed to wait a week(?) after all her shots...
Food, there are a lot of really good brands out there. Some pups are more pickier than others so it might be a bit of trial/error. Just remember, if you're switching food, you MUST do it gradually. Otherwise, she can get very sick. Link below is where you can find out info/reviews on all dog food (canned/dry). Personally, I feed my two Wellness for small breeds.
Dog Food Reviews and Ratings | Dog Food Advisor
Separation issue, in addition to yavenay's suggestion, try leaving the room for couple min and coming back. Try doing this several times a day. I saw this method used on tv and seemed to work really well.
Potty training... there's really NO easy method to this. Some pups know exactly what to do from the start, some are very stubborn. Does she have access to all areas? If so, try limiting her space. Are you placing pee pads in several places? You can also tether her so you know when she'll go. When you see her getting ready to pee, pick her up and take her to the nearest pee pad. Praise/offer treat (or toy). Are you planning to keep her on pee pad or will you be transitioning her to go outside?
No matter what method you decide to use, the most important key is to be persistent and patient.