And: Why are they allowed to advertise, but they have immunity from lawsuits?

HPV is a vaccine for human papilloma virus which is thought to cause cervical cancer. There are three types of vaccine HP2, HP4, and HP9. A few countries banned some of the earlier vaccines because of the seide effects, but the latest version fights more strains and seems to have lees side effects.

A big problem with the earlier shot is that it protected the recipient from a few selected strains, however, it had a negative effect if someone received the shot and caught a different strain of HPV. It attenuated the immune system so that the reaction to the strains not included in the vaccine became very severe.

A few countries banned the earlier vaccine because of high rates of neurological problems that seemed associated (I don't think it was ever proven).

The manufacturers have added more strains to the vaccine and it seems to be more effective with out as many side effects.

That being said....cervical cancer has an extremely low fatality rate in first world countries.