My mother had cervical cancer caused by hpv. She later had a hysterectomy at age 34 after I was born. Is it possible I contracted hpv from her?

No. If your mother delivered and did not have HPV caused venereal warts, then no. If you are now an adult, the HPV can from a sexual contact source.
Not at all. HPV strains are passed by direct contact to the involved structures. Occasionally the wart strains have passed at birth, from a birth canal shedding virus, showing up within 2 years on exposed genital structures. Childbirth does not expose a girls internal genitals to those cancer associated strains & we do not have any evidence that they are ever passed this way. They never travel in the blood.
Extremely unlikely. It is possible for a baby to be exposed to HPV during birth; however, this is unlikely to result in a long term infection or cervical cancer in you because your immune system will almost always eradicate it before it causes a problem. Cervical cancer is so rare prior to age 21 that we've stopped testing for it. Get paps and HPV tests as recommended starting at age 21 and you will be fine!
Not possible. HPV is transmitted through intimate skin-to-skin contact. You can get HPV by having vaginal, anal, or oral sex with someone who has the virus. It is most commonly spread during vaginal or anal sex. HPV is the most common sexually transmitted infection (STI). Pl see link to CDC's info page on HPV infection for details.
See here. Please see the following link for information.