This guide is a work in progress and is continuously updated with the help of the community. Pictures coming soon!
After completing the Mushroom Shrine theme dungeon, you can then raise the closeness of a number of NPCs that will allow you to use a skill once you reach a high closeness. To open the Threads of Fate window, you need to click the book icon on the left side of your screen, then click the mushroom shrine icon, followed up by clicking [Threads of Fate] Unraveling the Threads of Fate.
Talk to the NPCs in this window to gain closeness, and depending on how interesting the conversation is you will earn anywhere from +0-+3 closeness. Talking is limited, so you can't simply talk to them over and over to gain closeness. You must wait 1 full hour to speak to the same NPC. Also in the threads of fate window you can give gifts once daily to receive 3 closeness. You can equip up to 3 of these NPCs to gain stats on your Wings of Fate. Double click the NPCs while in the Threads of Fate window to equip them and their icon will appear in the area below. There are a couple of gifts that I don't know because I haven't unlocked them and JMS translations didn't provide useful info.
Mushroom Shrine Gifts:
+3 Closeness daily
Kino Konoko - Dolls from the mushrooms nearby Mushroom Shrine, they're called Sakura Mushrooms though they look like regular orange mushrooms.
Takeno Konoko - White, Red, Orange potion, or Elixir
Kamaitachi - Blue Dragon Hat, Pirate Hat, Thief Overall, Bowman Shoes, or Mage Gloves; all must be level 110-120 not any higher or lower.
Kurama - Regular arrows from NPC shops, Bronze Arrows
Ibaraki - A level 4 alchemy potion that enhances str, dex, int, luk or def; ex. Defense Potion IV, Strength Potion IV, etc. Any of these will work.
Nue - (Need 50 closeness with Ibaraki to finish the quest to unlock him.) Ramen from the NPC shop in Mushroom Shrine, Melting Cheese OR Reindeer Milk
Yorozu - Twisted Time, Alchemist Stones, Intermediate Item Crystals
Kubinashi - Lv120 Weapon (Warrior, Pirate, Demon weapon; accepts Briser Grim Seeker, may also accept the Briser Swords)
Izuna - Alchemy Flowers, Mandarin flowers confirmed to work
+3 Closenesss In Every Conversation:
It's important to note that once you reach 50 closeness, talking will no longer give closeness. I will be listing the conversation options in order. The first conversation choice for each NPC will have 2 choices. If you don't get the first choice listed below, press Esc and start the conversation again until you get that option. Can repeat the same conversation hourly.
Kino Konoko - Mushroom shrine > Why doesn't Takeno come outside > I heard there were rumors OR Takeno Konoko > You really care about Takeno > Bread was safe
Takeno Konoko - Hobbies > By yourself > Comb your sister's hair
Tengu - Things you like > What does Yorozu like > So I've noticed
Kamaitachi - What sort of things do you like > Zipangu's beauty > Do you get many dates
Kurama - What you hate > Afraid of > Not everyone's going to like you
Ibaraka - Kamaitachi > Secrets > Were any other Yokai involved OR Human world > Likes about human world > More human than many humans
Nue - Likes > Takeno > Love at 1st sight OR Let's talk about Kubinashi > Let's talk about Kubinashi's past > Not even about her past as a commander
Yorozu - Tengu > Relationship > Fond of him
Kubinashi - Hobbies > What she does when she was alive > Good at sword
Izuna - Dreams > What's her dream > Yokai living in mushroom shrine
Adding these as they are found.
After You Reach 50 Closeness
After reaching 50 Closeness, your options are limited. You either give daily gifts for 3 closeness or you can do Tengu boss runs (or you can do both). Closeness decays by 3 each day even after you reach 100 closeness. Each Tengu boss run gives 3 closeness to an NPC of your choosing, and you can do it up to 5 times a day. That's 15 closeness per day. Tengu runs take time, though, so it's best to do them with a party. One run for me, without any missed action prompts, takes about 10 minutes. That means it would take 50 minutes or more to max out your daily Tengu runs. I would try to find one or two people to go with you on Tengu runs so that they are finished quickly.
NPC Skills Received At 70 Closeness
Kino Konoko - Summons Kino for access to a special shop. This shop has potions and scrolls for the Wings of Fate. The scrolls are: 100% success rate for 5 all stats, 50% success rate for 7 all stats at a 50% boom rate, 30% success rate for 10 all stats at a 100% boom rate. You can only buy 1 of each scroll. 24 hour cooldown. Shop does not reset after cooldown.
Takeno Konoko - Uses bamboo to recover 100% of your HP and makes you invincible for 5 seconds. 30 minute cooldown.
All of these effects occur at 100 closeness with all 3 characters. Anything lower than 100 closeness will yield a lower stat. Get your desired stat combination below and maintain 100 closeness with the 3 chosen NPCs by giving daily gifts and you're golden. Disclaimer: none of these numbers are confirmed. I got these numbers from the JMS version of this event, and GMS may have changed these numbers.
Kino Kinoko + Kubinashi + Yorozu - 4% all stats (the other %stat combinations only go up to 3%) Kino Kinoko + Izuna + Yorozu - +20 Atk, +20 M.Atk Takeno Kinoko + Nue + Izuna - +10% Max Crit Dmg Takeno Kinoko + Nue + Yorozu - +10% Min Crit Dmg Kamaitachi + Nue + Izuna - +5% Atk Nue + Kubinashi + Kurama - +8% Crit Rate Nue + Kubinashi + Yorozu - +8% Ignore Monster Def Nue + Izuna + Yorozu - +5% Boss Monster Dmg Kubinashi + Kurama + Izuna - +5% M.Atk
This guide will continually be updated as other information is discovered! Special thanks to the people of basilmarket for helping me compile this info thus far.