Questions about HPV / genital warts in someone who is HIV positive

[Tofu_8242]

I am a gay male. I have recently started seeing someone who is HIV+, but undetectable. Recently, we noticed he had a couple of internal anal warts. I also had anal warts the year prior, and I have been clear of them for about 4-5 months now. I have never had unprotected sex with my new partner in either top or bottom roles, and I have never had HPV show up on my penis.

Questions:

1.) How likely is it that his intra-anal warts are from me, given that I have never had HPV warts show up on my penis, and I have never penetrated him unprotected? I feel extremely guilty that it might be from me, but I've only had warts show up anally and as far has I know, his anus has never had contact with my anus (that would be quite a feat).

2.) He is undetectable, although neither of us have an idea what his cd4 count is. Will he have a harder time clearing the infection because he is HIV positive despite being on meds and is generally very healthy?

3.) Do HIV+ people who are on meds and are undetectable have immune systems that function the same or very close to uninfected, healthy individuals?