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: Plant 4 Adventurnips (2 hour food)
Act 2: Harvest 4 Adventurnips
Act 3: Get “thank you” ticket from the battle tournament (round 2), visit THIS PAGE for more info
Rewards: 8 Realm Runes
Act 1: Harvest 5 Spell Melons (plant this while you waiting for the chapter 2 quest, so you can harvest immediatelly)
Act 2: Collect 85 Paper Wrappings from harvesting any food
Rewards: Present Puppy
Act 1: Win Round 8 battle tournament
Act 2: Harvest 6 Adventurnips
Act 3: Raise Puppy to level 5
Act 1: Breed Fairy Ferret with another animal
Act 2: Raise Present Puppy to level 8
Act 3: Collect 75 wrapping papers from harvesting any food on farm
Act 1: Plant 6 Mana Banana
Act 2: Hatch Chromadile
Act 3: Raise Present Puppy to Lvl 11
Rewards: Stars and 20000 Coins
Act 1: Feed Chromadile 25 times
Act 2: Plant 6 Mana Bananas
Act 3: Raise Present Puppy to Lvl 15
Act 4: Get “ticket” from round 16 battle tournament
Rewards: Santa Helpurr
Act 1: Plant 4 Rune Prunes
Act 2: Feed Chromadile 20 times
Act 3: Raise Santa Helpurr to lvl 4
Act 4: Get “ticket” from round 24 battle tournament
Rewards: 12 Runes
Act 1: Hatch a Turtisle
Act 2: Plant 6 Mana Bananas
Act 3: Raise Santa Helpurr to lvl 7
Act 4: Collect 100 Tape Rolls from Harvesting any food on farm
Rewards: Wrapping Station
Act 1: Feed Turtisle 30 times
Act 2: Raise Santa Helpurr to lvl 11
Act 3: Harvest 6 Spell Melons
Act 4: Get “ticket” from round 32 battle tournament
Rewards: 8000 Apples
Act 1: Plant 6 Adventurnips
Act 2: Breed Turtisle with another animal
Act 3: Collect 115 Tape Rolls from harvesting
Act 4: Raise Santa’s Helpurr to lvl 15
Rewards: White Elephant
These guides are taken from the storm8 forum. Thanks to people on those forums (Clark_Wayne, Alideh, Cardinalpsy)