You do not need to spend facebook credits to finish any quest. Items that can only be purchased for credits are optional.
If you have found a quest and you think it requires you to spend credits read it carefully again, including the tip. If it requires buying something remember that there may be multiple items that fulfill the quest and they may not be grouped together.
Sometimes the "ask friends" buttons for a specific building material will go missing from all quests, games, buildings, and/or machines. If this happens please post here or contact the developers directly. All building materials should have an "ask friends" button except for vitalin gems - vitalin gems can not be gifted but you can get one every 20 hours by mining vitalin crystals.
Specific Quests:
Dr. Cat's Sweetie: you can purchase
any cat statue. The Tigerseye Cat Statue is 3200 coins. It's currently on the same page as the picnic umbrellas, Rattleyrs, and Emerald Cat statue, but things in the shop tend to move around.
What's a Party Without Music: There's a new song "Bring Your Dancing Shoes" in Calliope, to find it click the Calliope, then "Play Song" then click the yellow arrow to the left of the songs.
New Tune: There are songs available for credits, and songs that require coins and sheet music. The number listed for sheet music may be how many more are needed than you already have.
Bonus Quests: Some quest chains now have bonus quests on the end. Such as "Tunnel of Love". These quests either involve items that require a large amount of gift-only items (ie 119 sugar skulls to buy the Haunted House") which allow players to either pay the usual price (ie buy 119 sugar skulls for credits) or earn some or all of them by annoying their friends. Or the quest may be for a credit-only item and give a special item as a reward (such as Tunnel of Love). These quests do not block any normal quests and can be abandoned (possibly not until the season is removed from the game).
NEW! Materials:
Not all materials drop, some can only be gifted. Not all materials can be asked for, gifted, or put on the wishlist. Some materials drop from both your own fair and your neighbours, some drop from your own fair only, and some drop from neighbours. Some materials can only be created in-game through "crafting" (in the Ore Refiner, etc). Some materials are only rewarded by quests.
ALL materials can be obtained without spending credits, though of course you can buy almost all materials with credits should you chose to. Most materials will tell you where they can be obtained from if you
Artesian water was the first material in the game that could not be gifted, it also could not be obtained from neighbours.
Gumbo, Cotton Candy, Peanuts, Bug Shoes, and Bug Whistles can not be gifted, but drop from both your own trees, neighbours' trees, and neighbours' protectors.