Can you have TCAS RA if your other traffic only have TCAS TA?
If both aircraft in an encounter are equipped with TCAS and are operating in TA/RA mode, then both will receive a coordinated RA.  That is the RA will be coordinated between them using the Mode S datalink.  

If both aircraft in an encounter are equipped with TCAS and one is operating in TA/RA mode and the other in TA Only mode, the one operating in TA/RA will receive an uncoordinated RA and the other will receive a TA. In an uncoordinated RA, the TCAS will provide guidance based on the observed path of the aircraft, modifying the RA as necessary.  

If one aircraft in an encounter is equipped with TCAS and operating in TA/RA mode and the other in does not have an operating TCAS, but does have a transponder, the one operating in TA/RA will receive an uncoordinated RA.  

There's a good guide to TCAS available from the FAA web site.