As i understand it, in order for an aircraft to be able to resolve a possible conflict both aircraft must be mode S equipped.
To have an indication of aircraft altitude on your own TCAS display the other aircraft must be at least mode C equipped. if it has no mode C ie mode A only you will get a symbol of an aircraft generated in the position it is in relation to your self but no altitude info and therefore no conflict alerting.
As for TCAS III, I think (and correct me If i am wrong) that it is still in test phases and I am not sure that it has been fitted to any commercial airliners as yet due to the accuracy levels it requires.