Hello,
"Is it worth it to level up to 20 ?" : reaching level 20 unlocks instant taming (not requiring a taming totem, yet consuming more stamina), also if it's a game+ new dresses will also unlock.
"can't find recipes" : any recipes that are still not learned/found can be purchased by interacting with Black Hair tamer girl, then pressing Q 2 times. All learned recipes can be checked in [TAB] Book > E > Left Right
"capture slime" : if you learned/found the recipe then it should be in Fapestiary ( [Tab] Book > E key > Left Right Keys). To capture a slime: insert a condom > have a vaginal finish with a male (to fill that condom) > get in the water with slimes (mofu plains or mofu lake) > while in h-act (she attacked you) press Q > carry the slime to the taming spot (press Q when she struggles)
"capture fairy" : after completing the fairy quest from TC it's recipe is auto-learned and stored in Fapestiary [TAB] Book. To capture a Fairy, the player must approach beneath a fairy x spider, and interact when they are finished with h act, or if H STop skill is unlocked - hold left shift and interact (consumes stamina).
Cheers ;)
~NK