The hiv antigens that are used in the oral rapid tests, are they infectious? The tests do not contain any actual virus but I am curious if the antigens themselves could somehow create the virus on their own if they get into the bloodstream? Like do they contain all of the parts needed for replication inside them? (Not the actual virus but the antigen).
nope - the test contains antibodies to HIV proteins, but nothing from HIV itself. The 'antigen test' tests for antigens, it doesn't itself contain any antigens.
Antibodies are proteins that animals (like humans) produce to fight of viral and bacterial infections, they don't come from viruses.
Even if the test did contain HIV proteins, it could not infect anyone. You really have to have the HIV RNA, and almost certainly the rest of the virus too, to cause any infection.
No, the protein components of viruses may be able to initiate the infectious process, i.e. injection, but if there is no RNA or DNA, there is no virus to inject into the target cell. Hence none of the viral genome's action such as replication or transcription will occur and the cell itself will remain unchanged.
However, some effects of viral infection are actually part of an immune response of some kind, and these are often triggered by viral proteins themselves.