I would like to create a slave site using a unique template and menus and custom code in my jomsocial directory.

How can I do this ?

Thanks

See tutorial video CP-05 that show how to create a slave site with specific template folder.
See also the tutorial 0.b slide 34 that show the differnt cases for the templates folder parameters.
www.jms2win.com/tutorial#jms12x-CP-05
www.jms2win.com/tutorial#jms12x-0b

The menu are never shared. So I don't understand this part of the question.

Concerning the custom code in JomSocial, they will be shared for all the slave site as I remember you that you share all the PHP code between all the websites.
So if you want to have specific code only called for a specific slave site, you have to program it inside your specific code.