So after little investigations I came to this:
The information in logs refers to problem with theme.yml file. As I go to search for it, I noticed that classic theme folder appeared to be renamed in the '/themes' folder (I don't remember why I did this). I changed the name of the folder back to "classic", so now everything is supposed to be fine, the .yml file is on it's place, it says name: classic; display_name: Classic in the beginning.
But I'm still getting a 500-crash of both back and front offices.
What should I check now?