1) I use ~/build/ for unpacking tarballs and building stuff from source. It works for me and I keep my downloads in another directory to keep things clean. Whatever you're the most comfortable with.
2) Most programs that you build from source will install to /usr/local/bin - the /usr/local tree is where you're supposed to keep locally built stuff but you don't *have* to. Although, it helps since most distribution-supplied software installs to /usr, so if you install your locally built stuff to /usr/local you will not over-write any distribution files.
3) You can delete the directory but I recommend keeping at least the directory itself and the Makefiles in it and its subdirectories. This way you can easily backtrack what files that program installed and often the Makefile supports doing a "make uninstall" to remove the installed software from your system.
4) See nr 3.