I’ve also seen a variant where the king isn’t (necessarily) the real king. Each player before the game secretly marks the bottom of whichever piece they want to be their actual “king” that game, and the game is won when a player captures their opponent’s marked piece. Pieces otherwise move normally though I think this mode is typically played without the rule that you just not end your turn with your king (the secret or public one) in check.

More casual way of saying asexual. Sounds a bit less clinical than the full term.

It varies within the genre. Some games try hard to take steps to minimize the ability to sit around and grind, such as by a food clock or lack of respawns. Sil, which is a *band game that tries to be closer to the original style has an XP system that grants XP for seeing an enemy the first time, and the same for killing it, and then 1/n times that XP the nth time you see that same kind of enemy thereafter. Sixth orc you see is worth 1/6 the XP, so it’s not worth farming an area hard, and still rewards exploring a lot. It also eventually just forces you deeper as the desire for a silmaril becomes more irresistible as you become stronger. Seeing 6 orcs and killing 2 is worth 3.95x an orc’s stated XP, seeing 30 and killing them all gets up to almost 8x the stated XP.

Others like most Angband variants or Tales of Maj’eyal made the decision to just let the player grind. Many of the games in that style have more open-ended progression and aren’t necessarily trying to force the player into constantly dangerous situations. The very popular Caves of Qud would fit this category.