So, I did it, and it was such a relief! It took me about one hour and a half to complete everything, both download and installation. Everything went smoothly, without problems and without unnecessary delays. Maybe because I have Intel installed graphics, I don't know.
Anyway, I just followed simple advices (keep old files, install Grub to /dev/sda). I checked everything after restart and, here it is, alive and kicking. I am even satisfied with the new fonts in Mate! Folks, developers, well done once again! I am just a little mouse, but it makes me proud to be a member of the Mint society.