If you are in contact with a child with chicken pox, but you are immune, will you carry the virus and pass it on to another child?

Very unlikely. The virus is transmitted primarily from actively infected persons who are making large numbers of virus in their systems. If you are immune you will not get the virus, and it will die quickly if on your hands, etc.
Not likely. Not likely but if you came in contact with the contaminated mucous you could potentially pass it on but it would have to be immediate.