Installing system files in home directory?
The answer to all your questions is No

To understand the file system you may like to start with File System Basics.

The three /Library locations are for different purposes though, as you have guessed, there is some overlap.

Briefly, the purpose of each is:


/System/Library:  Files which allow OS X to start and run.
/Library:  Other important system and application support files which are not specific to each user.
~/Library:  System and application support files which are specific to the user.


So files in /Library/Application Support/x are used by all users of application x and those in ~/Library/Application Support/x are specific to the user.  Some applications will only use one or the other, whilst some use both.

Moving folders/files between /Library and ~/Library is likely to cause applications to malfunction or system components to fail.  Moving LaunchAgents or LaunchDaemons is especially dangerous. 

Even worse, touching /System/Library is likely to prevent your Mac from booting!

Also, files inside application bundles must remain where they are - moving them will break the application.

So, in conclusion, don't move folders around as OS X expects files to be in their right place.