1) Before, from the very beginning and in present I was using web version hosted on virtual hosting. So, similarly to official Twine online editor.
2) Windows 10 x64, last update(I am not sure which one is last but I don't have any new updates yet).
3a) Google Chrome, last version: 63.0.3239.84
3b) No I haven't. I don't know why, but I thought this won't help anything yesterday. Maybe, because I was very angry... Just tried Firefox and it works there perfectly.
I was getting a lot of weird problems with Chrome lately, I am thinking it isn't worth any more to stick with it... But... It is not that easy...
Ok, next I tried incognito mode in Chrome and it also fixed this problem. I backed up my stories and went to the Chrome settings and removed all the cookies for the website and Twine. I disabled every extension aaaaand... Guess what? WRONG. It hasn't fixed anything! Omg.