Does the same HPV cause cancer in everyone?

Most HPV infections do not progress to cancer. It takes years to decades for an HPV infection to progress to cancer.

No the 'other' girl will not get cancer because they slept with the same guy and both acquired the virus. The virus is very common. Our Pap test monitor our cervix. When severe abnormal cell changes of the cervix are found a treatment is recommended preventing most all cervical cancer.

A person with a compromised immune system make keep the virus longer.

The answer is similarly hard to word... Kinda, sorta, not really.

Certain strains of HPV are more likely to cause cancer than other strains. If you catch HPV from a person who got HPV-related cancer, you are more likely to be diagnosed with cancer.

But most cases of HPV don't cause any cancer (although the majority of genital area cancers are correlated to HPV)

So, NO, this person wouldn't "definitely" get cancer. But they are at a higher risk for getting cancer.

Depends on the immune system of the host. One person's body may be able to fight it off and the other it may take hold.