/usr/bin/ld: cannot find -lX11
This error usually means you don't have the libX11.so library installed on your system. Which distribution are you running on? On my OpenSuse 11.1 the shared library /usr/lib/libX11.so is provided by the package xorg-x11-libX11-devel but it can be different for other distributions.
Regarding your second question, you can compile the source code in any place then copy the executable somewhere in your path. /usr/local/bin/ is a good choice. Take in mind that the installation of astrolog is atypical: it just build the executable and leave it in the current directory. It's up to you to copy it in a directory included in your PATH.
On the other end, the most common method to install from source requires three steps:
and the latter usually copies (installs) the compiled files in the proper locations, but always depending on the choice of the developers. They should be /usr/bin, /usr/lib, /usr/share/man, etc. or /usr/local/bin, /usr/local/lib, /usr/local/share/man, etc. However you can take control of the installation directories using the --prefix option in the configure step.
Furthermore, as a general rule it's safer to not delete the source directory, unless you have problems with disk space. This is because if you decide to uninstall the software, you can usually do
from the source directory itself, and every file copied in the installation process is removed from the system. Anyway, as I stated above, the astrolog installation does not follow these rules.