Question: I have a page I have to update, it has 3 frames (top bar, side bar and main content. If i click something in the main content frame i want to update a list in the side bar frame. how do i do this (i use jquery or javascript for button clicks).

Answer: 
*Q: multiplexing allows to reduce overhead of creating new connections to FCGI clients effectively interweaving requests chunks*

A: True. But keep-alive is also reducing new connections.

*Q: and at the same time enabling "keep-alive" model to connection*

A: Multiplexing is not required for keep-alive.

*Q: Latter allows sending several requests over a single connection*

A: keep-alive allows several requests after each other. Multiplexing allows several requests in parallel.

There is no widely used FastCGI capable web server supporting multiplexing. But nginx supports FastCGI keep-alive.

FastCGI multiplexing is generally a bad idea, because FastCGI doesn't support flow control. That means: If a FastCGI backend sends data, but the http client can't receive data fast enough, the web server has to save all those data, until they can be sent to the client.

When not using multiplexing, the web server could just not read data from the fastcgi backend if the http client is too slow effectively backlogging the fastcgi backend. When using multiplexing the web server needs to read all data from the fastcgi backend, even though one of the clients isn't receiving data fast enough.
I don't know if some server implement FASTCGI multiplexing (which I believe you understood correctly, but the details are in the FASTCTI protocol specifications), and I would not bother.

You will very probably use FASTCGI thru an [existing FASTCGI library](http://www.fastcgi.com/drupal/node/5) (e.g. [Ocamlnet](http://projects.camlcity.org/projects/ocamlnet.html) if you code in Ocaml, etc.). And that library would do the multiplexing, if it does it. From your point of view (of that library user) you should not really care, unless you are coding such a library yourself.

If FASTCGI multiplexing bothers you, you might use the [SCGI](http://en.wikipedia.org/wiki/Simple_Common_Gateway_Interface) protocol, which offers similar functionality, but is simpler, a bit less efficient, and non-multiplexing.