1 - Yes, there is a possibility, but there would be this possibility if you had sex with anyone. HPV is incredibly common. It's estimated that 90% of us will get it at least once in our lifetimes. Condoms offer significant protection against it, but not 100%. It can take several months for symptoms to appear, if you get symptoms.
2 - Probably not, if you haven't had any symptoms at this point.
3 - No. You have done all the tests, and you used a condom. As I said in a previous post, the only STDs you may get are syphilis, HPV and herpes.
You don't need to do another HIV test. You used a condom.
I don't know what the red spots were, but they were not related to an STD.