why did haymitch accept himself to the hunger games? Also, why does Gale think that Katniss likes Peeta?

Haymitch is a former winner from a different competition. Gale thinks that Katniss likes Peeta because that is the propaganda the organizers want o put out.

Haymitch is a former winner from a different competition. Gale thinks that Katniss likes Peeta because that is the propaganda the organizers want put out.

Only because they chose him. He probably didn't have a choice whatsoever.