Rests, Time Jumps, Exhaustion

"Take 10": In situations where there is no pressing rush for time, a player may "take 10" [minutes] to conduct an activity (such as an investigation check for traps around a door) to automatically pass the skill check. (To emphasize: not relevant in Initiative or time crunches such as, say, a guard actively chasing you.)
Take a breather: A character may "Take a breather" and rest for at least 5 minutes to catch their breath, slake their thirst, or check a single wound to bandage. During this time, they may regain hit points equal to 1 Hit Die + their Con modifier.
Short rest: Only change from PHB is a note that characters may remove 1 Exhaustion level per short rest.
Long rest: Only change from PHB is a note that characters remove 1 Exhaustion level per short rest, and gain 1 Exhaustion level if the character is unable to sleep/rest somewhat comfortably or do not have access to water and at least 1 ration.
Full rest: A character may take a period of downtime of at least 24 hours during which they sleep, perform light activity, or nonstrenuous physical/mental labor for less than 2 hours. This may not be attempted in the wilderness, while sleeping on uncomfortable dirt/stone, when wearing armor, or in an unsafe location (where a character feels the need to stay vigilant or keep constant watch). A full rest provides all the benefits of a long rest but reduces Exhaustion by 2 level instead of 1.
Exhaustion:

• Being stabilized after dropping unconscious (0 HP, making death saves etc.) yields one level of Exhaustion (per time being knocked unconscious, at DM discretion).

• Rolling Hit Dice during a long or full rest and rolling double the Hit Dice number (ex: rolling 12 points between 2 or more d6 Hit Dice), cleanse one level of Exhaustion.

• DM may add other instances where Exhaustion arises, such as when a user gets sick, or exerts themself in a way they are unaccustomed (a barbarian at a fancy gala, a frail wizard climbing a mountain)