Maps are optional. If you can’t find the place, just skip it. The pickaxe/cave-in was a part of the cut content. Just ignore it.
Some quests are tied to the main quest progression. If I remember correctly, Bully is one of them.
Most of the girls’ hearts, except for starting ones, are tied to their quests and activities. If I remember correctly, both Naka’s and Mariam’s are tied to the mysterious tower that will appear later in the game.