1. STDs like Hiv, Hepatitis, Chlamydia, and gonorrhea should be okay since the penis head is covered?
Yes, for sure
2. How likely is my risk of herpes/Syphilis?HPV?
I would say low. Condoms reduce transmission of herpes by 65% and the others, a similar amount. Most every sexually active person has had HPV of one kind or another.
3. I recently broke up with a girlfriend but plan to get back together. Can I proceed to have unprotected sex with her, or should I get tested?
I think testing is not necessary from a medical point of view, and don’t test for HSV, given high rates of false positive, but yes to syphilis and the other ones except HPV to eliminate and possibility of infection for you and so you can come back to your girlfriend, feeling really certain.
4. How would you asses the situation, and should I be on the lookout if symptoms develop, lest, say, the base of the penis or pubic area?
If you develop symptoms at the base of the penis, have them swab tested right away. I doubt that you will.