for the lava cave i will assume its the quest to unlock the tentacle wall, first desert needs to be unlocked first, then from there go to the east side of the desert where you found oasis, there, there's several cave you can enter, each one contain character for different quest, the scorpion for unlocking prostitute secret move, the helmet girl "boss" (you probably needs the dancer available to recruit first), an ice fragment boss for the frozen water fairy quest, and lastly earth elemental sword for the 4 elemental sword girl, after you talk to helmet girl boss, go to the mountain village where you first meet pink kung fu outfit loli, talk to the leftmost NPC behind counter and enter the stairs down, after fight the tentacle wall on the lava cave should be able to be destroyed (its dancer and helmet girl combo H-scene)
as for futa fairy village you must renovate east side of the base and gave the NPC asking for certain clothing on the mercenary town first, the certain clothing is onmyouji outfit, i forgot if that's from boss drop or chest, but it could be bought on floating island where you can buy dragon blood material and all status ailments null accessory, after giving the outfit the NPC will gave you miko outfit and the location of the forest, after unlocking the forest just keep walking until FMC notice she's walking in circle, then go back to base and enter the east building and read one of the book, after that get fairy leaf (its from collection point sparkle from the same map also a mob drop) and go to the paired red flower near water on the entrance map, and you'll unlocked the futa fairy village, if you go north there's special dungeon for the 4 elemental sword girl but it needs the earth elemental sword first to open the entrance
