Yeah, that quest log icon is just a placeholder. We just found out recently that viewing my guide on mobile demands you to have Google Docs installed... it is free, just download that real quick and it should open, see if that enlightens you on the quests and the gallery scenes (those are at the bottom, you can ask here for more info if needed). Other routes have... kinda obvious consequences, yes, the game can be enjoyed perfectly fine by picking just one route, of course, even if i like the focus on chars and strong moments the other three offer too.
The gallery wiping after you close the game sounds like a mobile issue, the data for them should be stored in the persistent save, try to save just after you unlock them all, close and open again... idk much about mobile myself, Caro on the discord can likely help. And yes, every scene until the "coming soon" ones can be unlocked by playing (a couple in the bull route only if you date Axel, a couple if you are dating Nauxus, which is possible in neutral too) and the cheat codes include an instant full gallery unlock, if you were referring to that.