All 4 difficulties of the labyrinth reset at 00:00 UTC, changing both the layout and Izaro phases.
Shortly after the reset the team over at poelab.com publishes the new layouts.
Atlas objectives have a 20% chance to be generated when completing a map. In addition to that, they regenerate each midnight at 00:00 UTC, just like the lab. There can only be one objective for each master active at once – new objectives replace the old ones. The objectives generated at reset will spawn on maps at approximately the same tier as the last completed map in that league.
Completing the atlas objectives may be desired, not just because of the mission reward, but because the inventory of that master also will reset. Therefore, a valid tactic, particularly in SSF where vendor rewards may be more useful, could be to complete a map in a tier where you have many maps available before the reset to make sure you’ll be able to complete it easily.
New Daily Deals start each day at 16:00 Auckland, NZ time. Most of the deals last for one day, but for some weekends they run special deals that last the entire weekend. The Super Stash Sale is probably the most sought for weekend special, that usually appears at least once a month.
The Path of Exile wiki has a list of all current and historic daily deals.