Welcome to the forum. I'll try to help.
You have learned a lot about these issue and your questions are thoughtful. But I think you failed to understand some basic aspects of HIV evolution and diagnosis.
The genetic and antigenic differences between strains are great in one sense, but the core genes and the proteins for which they code are in fact quite stable. There is no material difference across strains for p24, gp120, or gp41, the main antigens used as the basis for the routine HIV antibody tests. These determinants were chosen as the basis for testing in part because they are very consistent across strains -- or if there are differences, they are not sufficient to materially influence their ability to bind to antibodies directed at them, which is the biochemical basis for antibody testing.
To the extent that evolutionary changes of such a degree that the current tests didn't work might someday evolve, it has not yet happened to any significant degree -- and to my knowledge has never been found to have happened in industrialized countries or anywhere in the world except where HIV originally evolved (and continues to evolve), i.e. parts of tropical Africa. Ongoing surveillance in those areas almost certainly will be successful in identifying such HPV types and strains long before they are likely to be imported to other parts of the world.
Finally, in contrast to the assumption behind question 2, it isn't difficult to detect new strains when they occur. As already suggested, the standard antibody tests can be expected to detect such infections. Second, when there is serious clinical suspicion of HIV, both antigen detection tests and assays for HIV RNA/DNA in blood are done, and these are largely independent of strain differences.
For all these reasons, people concerned about HIV risks and the reliability of the current tests should have absolutely no worries. Follow safe sex guidelines and, if the need for testing arises, trust the tests. They work just fine.
I hope this helps. Best wishes-- HHH, MD