I am assuming you run kicad version 5. If you run kicad version 4 it gets a bit trickier.
KiCad does not care where you put them as long as you tell it where to find them. (Via the library managers. The library managers are found in the preference menus of the footprint and symbol editor. (The one in the footprint editor is for managing footprints the other one for managing symbol libs.)
Use the browse button to add libraries. (A file browser will open. Navigate to where you put your libs. Select multiple libs with shift plus left click or crtl plus left click.)
They should be. If you had kicad 4 installed previosly, kicad might still be setup for these libs. (Details about that can be found here in this FAQ article) Check it using the library managers i mentioned above.
You will not find footprints and symbols for every imaginable part. Furthermore you might have special requirements (example hand soldering) that might not be fulfilled by other libs. We have a tutorial for how to create footprints in our FAQ
No you can save them wherever you want. (As mentioned above you just need to add your personal libs to kicad via the library managers)
I would not suggest to put personal libs into the install directory.
You can of course add personal libs to the project directory. This makes the most sense if the parts in the lib are project specific. (For example if you make a specialized connector symbol that shows in the pin names which pin is used for what.)
Yes by having it in a library that you add to the global library table.
Some other helpful FAQ articles: