I personally think it is very unkind and uncouth to say anything like that to a senior citizen. It reminds him/her of impending mortality. The subtext is, "I am amazed you are still alive!"

I think "If you don't mind me asking" is more common, but "If you don't mind my asking" is also correct. I would phrase the second clause as "what's your secret to living a long life?"

Kurt answered as I would have as a native speaker.

"If you don't mind my asking" is perfectly fine. The second part could also be "what's your secret for living a long life".

Sure