The number of strains came from the CDC, take it up with them.
The vaccine only provides temporary protection. It has a significant rate of problems.
My knowledge of HPV comes from having done research in the field, not from looking at CDC articles. There are over 100 HPV strains, many of which cause cancer.
As far as vaccine problems, I’ve only seen that problems were reported as occurring after vaccination, but not that vaccination caused the adverse events. Any population has a certain level of adverse events; to implicate the vaccine means showing that a specific type of event occurs at a significantly higher rate than in an unvaccinated population.