The rule is that you must touch in and out when using PAYG, and any journey that travels outside the zones of your travelcard is by definition a PAYG journey (part covered by the travelcard, yes, but the journey still requires PAYG).
Yes, but (for the travelcard mentioned earlier, at the stations mentioned - New Malden and Richmond I think) one could 99 times out of 100 avoid touching out at New Malden.