Shortcut to Mushrooms's last ability will trigger only once during your end step, no matter how many permanents you controlled left the battlefield this turn. However, if no permanents you control have left the battlefield so far this turn as your end step begins, the ability won't trigger at all. It's not possible to cause a permanent you control to leave the battlefield during the end step in time to have the ability trigger.

The Ring can tempt you even if you don't control a creature. In this case, abilities that trigger "whenever the Ring tempts you" will still trigger.

As the Ring tempts you, you get an emblem named The Ring if you don't have one. Then your emblem gains its next ability and you choose a creature you control to become (or remain) your Ring-bearer.

Some spells and abilities that cause the Ring to tempt you may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won't resolve. The Ring won't tempt you.

Shortcut to Mushrooms doesn't need to have been on the battlefield when the permanent you controlled left the battlefield. For example, if a creature dies during combat on your turn and you cast Shortcut to Mushrooms during your second main phase, its last ability will trigger at the beginning of your end step.

Each player can have only one emblem named The Ring and only one Ring-bearer at a time.

Each time the Ring tempts you, you must choose a creature if you control one.

The Ring gains its abilities in order from top to bottom. Once it gains an ability, it has that ability for the rest of the game.

If the creature you choose as your Ring-bearer was already your Ring-bearer, that still counts as choosing that creature as your Ring-bearer for the purpose of abilities that trigger "whenever you choose a creature as your Ring-bearer" or abilities that care about which creature was chosen as your Ring-bearer.