1. There is a PATH variable in linux also. If a directory is in your PATH, then you can run binaries just by typing their names. I believe the PATH is set for all users in /etc/profile and for individual users in .bash_profile.
2. I think it depends on the desktop environment and/or distro. KDE has KControl Center. I'm sure Gnome has a Control center also.
3. I think it lives in control center.
4. Program files can be installed anywhere, but typically programs are installed to /bin or /usr/bin. System programs are usually in /sbin or /usr/sbin. When you compile a program from source code, many people install it to /opt just so they know it's not a regular installed program.