> Honest question... if HIV is a virus, and virus are not living forms, how can they evolve?

The requirements for evolution are a subset of the requirements for "life", so its quite possible for things that are not alive to evolve.

> In that case wouldn't be the host cell the one that evolved?

Viruses can be a source of variation in the genetic code of living things that contributes to evolution in the living things, but that's a different effect than the evolution of the virus itself.

Evolution does not strictly apply to living organisms. Natural selection, which is what I think your referring to, as a mechanism for evolution relies on Mendelian inheritance. The only requirement for Mendelian inheritance is genetic material (DNA or RNA), which viruses obviously have.

No, because the host cell is generally used to produce more viruses and is then lysed to release them. HIV and other retroviruses use RNA to inject DNA strands into the host cell's nucleus where those new genes instruct the cell to produce more viruses. Even if the host cell splits, the genetic machinery is still there for the virus to reproduce.

Either way the end result is a bunch of new viruses each with their own genetic code that could have mutated.

AFAIK whether or not viruses are living organisms is the equivalent of programming language religions in biology and is quite controversial. I personally look at viruses as living organisms and consider "viral reproduction" amongst sexual and asexual reproduction.

Evolution is about replicators. Living things tend to be replicators, but not all replicators are living.