If you still have an ovary it could be possible. Talk to your doctor.
It's very rare that you get pregnant after a partial hysterectomy. You would get pregnant through sex just as you would before your hysterectomy. Again, this is very rare.
If you still have your cervix, you will lightly bleed once a month. Google it for more indepth answers.
No.
Yes, and even after a total hysterectomy, even though the uterus won't be involved.