1. The quip was that people who don't want to get vaccinated will get immunized through infection. Yes, using "vaccinated" in this context ("the variant that will vaccinate") is not proper usage of the term unless we allow the interpretation that vaccines are milder than the disease and Omicron might be milder than Delta.

2. "obscure, experimental, for older strains": Look, the vaccines are not obscure. Billions had them. Experimental: Sure. Much as not getting vaccinated is. Remember, we haven't seen that virus before. Older Strains: Turns out protection against severe effects is still strong. I'd say experimentally you're better off partially immunized with one of the well-known vaccines than when waiting around for one of the variants to catch you naive.

GP meant that they will just get infected and thereby acquire a degree of immunity, with higher risk of death than the vaccine, but (hopefully) not as high as with previous variants.

I think the parent meant that people who had not gotten a vaccine will get omicron, which is hopefully mild, and will hopefully provide good protection. So they probably should have used immunize vs vaccinate.

Irrelevant. As the new strain outcompetes the old, the old dies away forever. For example, Delta became 99%+ of cases in the US.

Omicron evolved from Beta... so not really.