Abilities that begin with "At the beginning of your end step, if you descended this turn" will trigger only once during your end step, no matter how many times you descended this turn. However, if you haven't descended this turn as your end step begins, the ability won't trigger at all. It's not possible to put a permanent card into your graveyard during the end step in time to have the ability trigger.

Multiple cards have abilities that begin with "At the beginning of your end step, if you descended this turn." These cards don't need to have been under your control at the time you descended. For example, if a permanent card is put into your graveyard during your first main phase and you cast Stalactite Stalker your second main phase, its ability will trigger at the beginning of your end step.

An opponent with zero cards in hand can't choose to discard a card. Similarly, an opponent with no permanents can't choose to sacrifice a permanent.

In either case, it doesn't matter if those cards are still in that player's graveyard.

Some cards refer to a player who has "descended this turn." This means that a permanent card has been put into that player's graveyard from anywhere this turn.

A permanent card is an artifact, battle, creature, enchantment, land, or planeswalker card. Tokens are not cards, and while tokens are put into the graveyard before ceasing to exist, that action doesn't count as a player having descended.

Some cards refer to the number of times a player descended this turn. Those cards care about the number of permanent cards put into that player's graveyard from anywhere this turn.