The boosted dose is only for people who are assigned male at birth.
I take the PrEP brand truvada once a day which is effective for both sexes

I have immunity as long as I take it daily. Definitely confirm with your doctor before taking it, you need to have blood work done and regular HIV testing every 3 months
The gardisil shot should be taken for HPV. Most people born in the 2000s and on have had this shot already around middle school age, unless your parents refused it. If you have not had it you can get it and it is recommended. It decreases the risks of getting cancer even if you do contract HPV. This is one of those things that most people are a carrier of and never have active outbreaks (ie: warts) but you can still spread it and still get cancer from it.
Herpes is unavoidable and most people are carriers of the virus. As long as you never have an out break of symptoms, you kind of just have to accept it is a risk and not engage sexually with anyone having an active infection. But even then, you can still get it.
Most doctors don't test for it because the tests can show false negatives or positives due to the viral load being present in most people - they have to test it on a scale rather than a straight positive or negative. And, even then, it could still be inaccurate. A big viral load doesn't mean you will ever have an active infection - a small one doesn't always mean you can't spread it.
I have never had it so I am not sure what it is like but I have heard it is painful so it is highly unlikely you would not notice if you had an active infection.
As a general rule, remember to get a full panel test and specify with your doctor you want to be tested for everything because they do not always run full tests
I just learned from reading an article that chlamydia can lay dormant for up to 10 years with no symptoms! You can still spread it during this time meaning if you never get tested you would never know. Testing and communication is the ultimate protection