Does repeated anal sexual activity cause a woman to pee and poop more often than before she started having this type of sexual activity?

Intercourse. Anal intercourse does not cause changes in bowel movement per se. It may cause anal spinchter reduncancy/weakness (anus squeeze may not be strong enough causing you to have accidents aka-incontinence). Your are increased risk for hiv, other std and perianal infection/abcess due to significant mucosal tear due to harder friction.
YES. Stimulating of the anal sphincter can cause an urge to deficate. The urge to urinate is from pressure on the bladder.