Hm, it worked in my test. Will look into it later. Witch release are you using ? The windows one? Do you get the save icon in the right bottom corner, or nothing at all? 

I'm using the windows version.
There is no right bottom corner icon, only the new in the right upper corner, replacing the one from previous versions. I have two problems :
1 - I tried to play from my last save (evening the bedroom, only choice available being going to sleep or re-enacting the 1st sex scene with Melody), so i went to sleep but in the morning, on the picture showing the whole school, there was no icon appearing anywhere to click on and i was stuck.
2 - So, i tried to start a new game. For some reason, the save/load icon in the upper right worked, but intermittently. It seems the clickable zone on the icon works only for a small part of it (the lower part).
Maybe my two problems are unrelated. Apparently, clicking on the lowest part of the new icon (upper right) works, so problem #2 seems to have an explanation. I don't know about the lack of clickable things in the morning from problem #1.
Since there is still a single save and it automatically erases the previous one, i'm going to replay the whole game, and when i reach the point where 0.2 ended, i'll see if problem #1 reappears.

Thanks for your detailed description!
Problem one could be because the variables what to do in the next morning are set in the previous scene, but I am not 100% sure, have to check it when I came home later. Maybe I cloud add a small clickable object in the room that sets all variables straight to continue from the last games end. You should however be able to jump to previous saved checkpoints with the representative button, so you don't have to start from the beginning.
Problem 2 I have to look into it.

yeah, the update starts with a new (separate) chamber scene, so the decision to load that new scene is made on the map (before). If your save is already in the old chamber scene, you are kind of in a dead end, sorry I didn't thought of that. Again, if you have saves at previous checkpoints, you can jump between them with the Jump back / Jump ahead buttons. I am still eagerly waiting for the fungus update to implement the new save system which is going to be slot based but so far it seems they didn't make any progress according to their GitHub :(
I couldn't reproduce your 2. problem on my end. What resolution are you playing at?

i lowered the resolution, and apparently, the clickable zone now occupies most of the icon, so, it seems there was the problem.