Comprehensive guide to quests
Summary: You get a new quest every 8 hours, quest rewards vary from 1250 gold to 12 packs, on average you can expect ~2 packs worth of stuff per day in quest rewards but rewards can and will likely get very spikey. It is very unlikely that you get less than a daily average of 10k worth of stuff over a timespan of at least two weeks (the absolute minimum when not missing a quest spawn is ~9.2k with no uncommon quests and only the lowest reward rolls).
Here's the comprehensive guide to quests:
The map is divided into 6 regions each corresponding to one of the 6 aspects (colors). You start with only the order region unlocked and unlock the others by unlocking that color's starter deck.
Daily quest spawns:
Once every 8 hours - there's a timer at the academy - one of the six regions on the map, that doesn't have an active quest already (a quest you've already accepted), is randomly chosen and 1-4 quests will spawn in that region.
Of those quests you can choose the one you like best and the others will be discarded. This means you can only ever have one active quest at the same time in a specific region.
Quests will always spawn in regions that currently have no quests on them first. If all unlocked regions already have quests on them, a region that has no active quest and fewer unaccepted quests than the maximum of 4 will be filled.
This means that you can accept a maximum of 3 quests per day, if you have at least one empty region every 8 hours. Because there are 6 regions you can have 6 quests active at the same time, so you don't need to complete 3 quests every day to not lose out.
If you have multiple quests that require you to do the same thing (e.g. playing quick battles), your progress will count towards all of them (so you can complete 2 quests that require you to play 3 quick battles by playing just 3 quick battles).
The Academy is an extra single quest site located in the north of asperia and serves as the main hub for tutorial tasks and the source of rare and epic quests. The Academy itself is populated with quests independently from the other quest sites. It will offer you a quest of guaranteed rare or epic rarity every 3 days. The timer resets once you've either completed or declined the quest. Declining will reset the timer to 3 days and not reroll the quest.
Furthermore it displays a timer showing you when you'll get your next rare and epic quests in the other zones. Every 12-20 quests you complete the next regular quest spawn will include a guaranteed rare quest and every 30-42 it will include a guaranteed epic quest. These two counters are independant from each other, so every quest you complete counts towards both. However only the counter with the lowest remaining required quests will be displayed. Once you got a guaranteed spawn the corresponding counter will reset to a random number in its respective range. In the case both counters reach 0 at the same time you will get an epic quest next and the rare quest in the spawn afer that (this means you won't ever miss out by getting the rare and epic quest in the same region).
Like cards quests also have rarities: common (gray), uncommon (silver), rare (gold), and epic (blue). Quests of higher rarities will almost always require you to complete more difficult/more time intensive tasks, but they will always offer greater rewards. Note that while common and uncommon quests are random spawns, rare and epic quests spawn strictly according to the academy.
Quest rewards include but are not limited to:
Common: 1250-3500 gold; 1 small pack; 2 uncommon cards; 1 foil common
Uncommon: 7k gold; 2 small packs (10k gold value); 1 foil uncommon
rare: 10k+ gold; tickets (used for tournament and trial entry); 2 rare cards; 1 foil rare card
epic: 20k+ gold; multiple tickets; the 12 pack box (literally straight up 12 normal packs); 2 epic cards; 1 foil epic card
Quests that reward cards of a specific rarity will never give you excess cards of that rarity, so you won't get cards you already own 4 copies of as long as you don't already have 4 copies of every card of that rarity.