When a game says in the system requirements that it needs lib1 lib2 lib3 and such, does it mean that the .sh package will automatically install those libraries? Or does it mean that the user needs to install them manually before/after the game installation for the game to work properly?

Mostly user needs to install them manually, unfortunately, but! Sometimes some of these libraries are already in your system. :)

Do the installation in the terminal and you should get a list of libraries the game wants and cannot find. Now when you already have the library or a newer version but the game cannot find it or use it, then you are in trouble and you get the "Linux is hard to use" as the difficulty goes up.

No, you need to install them. That can became a problem though, as you can see here:

https://www.gog.com/forum/general/linux_32bit_game_olliolli_now_broken_help

I don't think any GOG installer installs packages. Otherwise you'd need to type in your password, wouldn't you? Oh, yeah. Have you been able to solve such issues?

Sometimes yes, other time no. Not such a super expert on Linux. When it screams it wants libmissing I check whether I have such installed, any version. If not, I install the latest for my system. Things get harder when I do have them but then the game either cannot find them or it does not understand the version I have becasue it is too new.

Sometimes it's tough. I was having a hard time staying productive when I was facing some challenges with immigration a few months ago. What worked to mitigate a bit for me was eating healthy, exercising, and trying to sleep regularly.