Will I still have feeling in my breast after breast cancer surgery?

Usually yes. If you have a lumpectomy, you still will have feeling in your breast. If a lot of tissue is removed from the area behind the nipple and areola you may loose some (or all) sensation of the nipple. If you have a mastectomy you will have numbness of the skin adjacent to the incision where they made the skin flaps to remove the breast.
Depends. This depends on the type of surgery that is performed. If the entire breast is removed (mastectomy), there will be minimal feeling. With a lumpectomy, generally feeling returns once everything heals.
Usually. If it is a lumpectomy, usually - although you may have areas of numbness or tenderness.