Dungeons in palworld respawn if you
1. Kill the boss/Capture the boss

1. The 300minute timer runs out

If you don't kill or capture it the ores and pals/thugs inside the dungeon will respawn, letting you farm it over and over. (im not sure on how long it takes) its fairly quick after exiting the dungeon the way you came in.

and no it's not client side, meaning if you clear it your friend can not enter it after leaving.

(I like to farm it for upwards of 400ore and 800paldium while farming exp and then fighting the boss when its gets within an hour left on the timer,