Short answers, pulled from the story.
The harem genre is a genre of light novels, manga, anime, and video games centered on a single protagonist surrounded by three or more potential romantic or sexual partners. It originated in Japan in the 1970s and grew more popular in the late 1980s and 1990s alongside the rise of dating simulator games.
The harem genre originated in Japan in the 1970s. Its popularity then increased during the late 1980s and 1990s as dating simulator games became popular.
A reverse harem flips the harem genre's usual setup, following a female protagonist pursued by a group of male suitors instead of a male lead surrounded by women. It targets a mostly female audience, in contrast to the mostly male audience for standard harem works.
A harem ending is an ending in which the protagonist of a harem story ends up in a polyamorous relationship with all of their suitors at once, rather than choosing a single partner.
Yes, the harem genre includes yaoi and yuri harem works featuring same-sex pairings. Kyo Kara Maoh! is a same-sex harem anime with a male protagonist surrounded entirely by male characters, and dating sim visual novels increasingly let players choose an opposite-sex or same-sex harem.
Critics argue the harem genre often portrays women unrealistically and at times misogynistically, since female suitors are frequently reduced to a single desire for the protagonist and one-dimensional traits. Critics also argue the passive protagonist trope reinforces a belief that men are entitled to female affection.