You can only finish one chapter per day, if you don’t want to wait you can simply skip it by using gems. only skip the first few chapter because the cost is still small (5 gems).
The waiting times is always different and it depends how fast you finish the quest. Here’s the explanation:
 The new quest is available on 00.00 AM PST (fantasy forest story server time).
 Let’s say you finish the quest at 23.00 PST time, then you only need to wait one hour before you get the new quest.
 If you finish the quest at 01.00 PST, then you need to wait 23 hours :).
Plant xx food: You only need to plant, the quest will be completed once you have planted the food (no need to wait the food)
Harvest xx food: you need to plant and then wait until you can harvest the food. You can plant the food, and then harvest them when you get the quest to finish it quickly. See the guide below.
Raise animal to lvl ..: You can raise the animal to max level, even before you get the quest. Don’t be afraid since the quest will automatically completed when you get it. HOWEVER, it’s different from..
Feed xx animals for xx times: Don’t feed the animal before you get the quest because it won’t be counted.
The quests below are for high level players; above lvl 30), so if your level is lower, then you may find the quests are different
Act 1: Harvest 5 Adventurnips
Act 2: Collect 1 Lamp from the mine
Rewards: 8 Realm Runes
Act 1: Hatch any animal
Act 2: Plant 3 rune prunes
Act 3: Collect 6 desert gems from evolving any animal
Act 4: Breed Chromadile with another animal
Rewards: Persian Leopard (earth fire animal)
Act 1: Hatch Persian Leopard
Act 2: Collect 32 magic carpet from harvesting (1 Carpet/hour food)
Act 3: Raise Persian Leopard to lvl 5
Act 4: Collect 2 lamp from mining
Rewards: 5000 Apples
Act 1:Raise Persia Leopard to lvl 8
Act 2: Hatch armordillo (12 hours earth fire… very easy to get 🙂 )
Act 3: Plant 6x spell melon
Act 1: Feed Armordillo 30 times
Act 2: Collect 50 Magic Carpet from harvesting any food (1.5 magic carpet/ hour food)
Act 3: Breed Racmoon with another animal
Act 4: Raise Persian Leopard to level 11
Rewards: 20000 Coins and 5000 XP
Act 1: Collect 4 lamps from mining
Act 2: Plant 6 Mystic Mangos
Act 3: Collect 8 Desert Gems from evolving (1 per hour)
Act 4: Raise Persian Leopard to level 15
Rewards: Winged Lion (lightning fire)
Act 1: Hatch Winged Lion
Act 2: Hatch Firefox (Fire + Dark; 9 hours)
Act 3: Raise Winged Lion to Lvl 4
Act 1: Collect 60 Magic Carpet from harvesting
Act 2: Raise Winged Lion to lvl 7
Act 3: Feed firefox 25 times
Act 4: Plant 6 adventurnips
Rewards: 10 runes
Act 1: Raise Winged Lion to lvl 11
Act 2: Feed Firefox 15x
Act 3: Collect 5 Lamp from mine
Act 4: Hatch Frostfang
Rewards: 7500 Food
Act 1: Feed frostfang 30 times
Act 2: Raise Winged Lion to lvl 14
Act 3: Collect 50 Magic Carpet by harvesting
Act 4: Breed Persian Leopard with any animal
Act 5: Collect 6 Desert Gems from evolving any animals
Rewards: Arabian Horse
These guides are taken from the storm8 forum. Thanks to people on those forums (Alideh)