It seems women are always being told they must/should undergo cancer screenings but are not given any risk/downside info as men are for prostate screening. Why? Shouldn't women be fully informed too?

Screening is vital. Screening for breast, cervical, or colorectal cancer can decrease cancer mortality. Although screening for these cancers is recommended by the uspstf, screening rates in the United States do not meet targets.
Yes. Maybe even more so than men. Women should discuss issues about breast, uterine, cervical and ovarian cancer with their doctors. Often genetic testing is helpful in determining a course of appropriate screening.