> Do you if it is possible to limit the access to the chat (all the channels) to a limited group of registered members by enabling the menu entry only for this group?
Yes of course! In version 1.8 and CVS you can assign menu options to only appear for a selected group or those based on permissions. In the 1.7.4/5 version I would recommend a module thats played on a group.
Or if you want you could even just leave the menu as is, and just give that group the tiki_chat permission.