MacOS User Library folder looks strange/fragmented -- folder = 'Library and folder = ' and folder = "

It appears to me that some of your folder names have been renamed with unusual names somehow - so to answer your question, no, this is not normal or correct. Can we try a couple of Terminal commands (Terminal.app is located in the /Applications/Utilities folder). Once you have started Terminal just type the following into the window (all Teminal commands are in the bold italic font so as to make them stand out):

pwd

ls -la | grep ^d | od -cx

The first command shows the current folder name - need to make sure it's your home folder, and the second command shows a list of all the current folders (things that have a "d" as the very first character of the "ls" output - which denotes a directory/folder and then it prints them in a way that will make it easier to see if there are any special characters besides ' or " in the names. If you reply with the output of these commands (just highlight it and then copy/paste from either the Edit menu at the top of the screen or use the keyboard shortcuts Command+c and Command+v for copy and paste respectively), be careful of including any personal info.

My guess is that somehow your Library folder in your user home folder has been renamed accidentally to have a ' character included as part of the name and you have a couple of other folders that have names ' and " -- none of which is normal. I'm hoping these last two folders with names ' and " are both empty so it would be possible to just remove them rather than try and figure out what they used to be named, but untill we know for sure better to be sure what's really in them. Same goes for the 'Library folder - hoping that it's real name should be Library but need to know a bit more to be sure.

In order to be sure of what they used to be it's gonna be neccessary to see what's in them so try this in the Terminal window:

cd \'

ls -la

and also

cd \"

ls -la

and also

cd \'Library

ls -la

The \ character (I call this a "backslash") is usually above the Return key on your keyboard and it tells the Terminal window to treat the next character as the actual character rather than have it be treated as a meta-character that the shell might treat in a special way. The | character is called the "pipe" character which is nomally above the Return key and needs the shift key held down before pressing it. You need to press the Return key at the end of each line as that tells the Terminal program to perform the command.

Be careful of doing stuff in a Terminal window as it's possible to do unintended things if you goof something up if you're not sure of what something means. None of the commands I have given here actually change anything, just look at the state of things in a bit more detail. If you're not sure of something - ask first before doing it. Better to understand fully than do something accidentally that might be difficult to recover from.

Good luck...

-bob