What is the function of shell

The shell is nothing more than a window into which you can type text operating system commands. It's the interface, not the operating system. Unix is the OS.

Back when Unix was written, there were no graphical user interfaces. That text shell was all that we had.

Other examples of inter process communication besides client/server? Point to point sockets, peer to peer might be another.

A shell is simply a program. In Unix, essentially any program can be a shell.

The shell can be the program set up to run when a user logs on to the system.Or the shell can be a program run from that program.

Normally, one thinks of a shell as being a command interpreter. The shell could be a graphical user interface. Or the shell could be some application to administrator wants to lock the user into.

Some systems, for example VMS, have the user interface component integrated into the operating system. The command interpreter (in VMS, DCL) runs in a protected mode and is generally available to applications. That is, if a program is started from the command interpreter, it remains available to the process. In other words, each time you run a program from the command interpreter is you remain in the same process. In Unix, each program run is a separate process.