This is the default user-level package library, it is possible to define a custom location for this if you want but under normal circumstances you would never need to manually access this files so I would recommend you to just leave it as is for the time being.
In case you really want to modify the location of your package library, here you can find how to do it:
Packages only need to be installed once with the
install.packages() function but they need to be loaded with the
library() function on each R session you want to use them.
RTools is used for compiling packages from source, you would only need it if the package you want to install is not currently available as a precompiled binary. For the latest R version (currently the one you are using) precompiled binaries become available a couple of days after a new package version is released so unless you are in a hurry to install an specific package version that is not currently available as a binary, you don't necessarily have to install RTools, although, there is no harm if you do.
The working directory is a dynamic concept, you usually set it per project to a folder containing the files for that specific project and you change it when you want to work on another project.
Although, if you are using the RStudio IDE, a better workflow is to create an "RStudio Project" and that will automatically take care of the working directory for you. You can learn about this workflow here:
I believe you are overthinking this, you should have a "root" folder containing all necessary files for each project you want to work on and that's it, under normal circumstances you shouldn't have to worry about any other folder, leave this issue for when it is actually needed, like when you get an error message saying it has problems with some folder location.