Your answer is correct. HIV-1 encodes a single homodimeric aspartic protease, with each monomer containing the classic Asp-Thr-Gly motif, and the dimer's active site being formed with the two monomeric active sites creating a cleft where the proteolysis takes place. In it, water acts as a nucleophile in conjunction with the aspartic acid residue to hydrolyze the peptide bond in the protein's target.
WikiMedia: Aspartyl protease mechanism.png
A number of HIV-1 proteins are synthesized as polyproteins, and protease is required to cleave them in the appropriate spot(s) so they can assume their mature forms. This is a very big deal, because without these cleavage events HIV-1 cannot complete its replication cycle, and so becomes non-infectious.
Protease inhibitors act by "sticking" in the binding cleft, obscuring the aspartate and preventing binding of the target proteins. However, these small-molecule inhibitors are very specific to HIV-1 and the amino acid residues that compose the binding cleft, otherwise they could potentially inhibit one or more of the many aspartyl proteases our body makes naturally. While it is not very likely that a destructive mutation in the Asp-Thr-Gly motif would result in a replication-competent virus, other more conservative mutations may occur in the binding cleft that still allow the target to bind and be cleaved. However, depending on the exact protease inhibitor being used, a single mutation, even if it's conservative, may still be enough to dramatically decrease the inhibitor's binding efficiency and allow protease to maintain some or all of its functional capacity. This is why cocktails of inhibitors are used: they each depend on different amino acids for their binding, so if mutations arise at some point that do affect the activity of one inhibitor, others may still be unaffected. Evolutionarily-speaking, the inhibitors put a tremendous selection pressure on the virus, which combined with HIV-1's naturally "sloppy" replication process, leads to mutants appearing in relatively short periods of time.
There are two kinds of epitopes in the adaptive immune system: those recognized by antibodies and B cells, and those recognized by T cells when presented in the context of MHC. Antibody epitopes are generally found on the surface of a pathogen or a pathogen-infected cell (when speaking in the context of infectious diseases), as proteins or other compounds capable of raising an immune response that are only located completely inside of the pathogen or infected cell are not available for binding. T cell epitopes, on the other hand, are linear peptide fragments (and sometimes other molecules, like glycolipids) generated by internal processing in the antigen-presenting cell, and are usually pretty representative of the complete contents of the cell, native and foreign. Native epitopes generally don't produce immune responses - when they do, autoimmunity occurs. Foreign epitopes are recognized by circulating T cells, and help prime an immune response against the infected cells. (As a side note, since HIV-1 infects a subset of T cells, it is a way for them to escape immune detection). Mutations in the protease protein may affect some of the epitopes it produces, but those mutations are just as likely to increase visibility to the immune system as decrease it, so overall there's no net gain or loss.