In general, the larger the colony, the more difficult and more rewarding quests will be. Quests use the raid points mechanic to determine quest size. With the Royalty DLC active, you will get 2 quests every 12 day interval, as this DLC introduces many more possible quests. Without the Royalty DLC, you will receive 1 quest every 10 day interval - this means that quests can be up to 19.9 days apart.

Some Quests, such the beggars quest, are accepted automatically The 3 endgame quests in particular (Ship to the Stars, Royal Ascent, Archonexus ) can be done at any time.

The second timer is the time to do the quest, or alternatively, how long a quest lasts for.

If not accepted, the quest will be rejected.

The first timer is the limit to accept the quest.

Most quests are time sensitive, and have one or both of these timers: Quests can be 'trashed' by clicking on the trash can icon, but is purely visual and can be reversed (Quests/Historical). Some quests have requirements to be accepted, and others have a time limit for acceptance.

Most quests have to be accepted, but some are automatically given. Most quests are offered by a faction, but they can be offered by individual pawns or unaligned AI's.

Survivors the quest lab notes