Absolutely. Even without a uterus (you don't mention whether your ovaries were left intact), you still need an annual pelvic exam. You may or may not need a pap smear depending upon your prior pap history, but you vagina, labia, vulva are all areas that need regular evaluation. Moreover, you should not have a mammogram done without first having a clinical breast exam by an experienced examiner, i.e., obgyn.
Yes you do. Vaginal exam and breast.
Maybe. For pelvic exams: depends on why you had the hysterectomy, did you keep your cervix or have it removed. You may still need paps. Other reasons: do you need hormone replacement? You need someone to watch your bone health, and need breast exam/ mammograms on a regular basis.