i have unfortunately had a lot of trouble with godot's IK constraints (which are what the character animation is based on). to summarize my pain: exporting the game, it had issues; i restarted godot and exported the game again, and it was fixed. this kind of jank... where something in the editor effects the export process, soemhow, is very frustrating to me, as i seem to have no control over it.
I do not have a linux computer, but i may try to re-export the linux version and test it in VM. when i run the current version in VM i do not see this exact issue (as the game is too laggy in VM for it to even flicker like that) but i do see some kind of IK related issue. so perhaps i will be able to at least half-verify whether a re-export works before uploading it. i'm also considering adding an option to just hide the sex animation as it's really not super important to the gameplay.
anyways, thanks for the bug report and for playing my game!
for your second point: i think this is likely not a bug, from looking at the gif. i am also not able to get through this puzzle when i move back and forth across three tiles. it should work if you only use two though!