Carol and I are [still] friends and even though she went moved back to the US a few years ago. We're still in touch and we sent send text messages to each other from time to time.
Silver - Will you ever come back to Chongqing? again?
Carol - Probably not. I'm getting older and I'm 78! this year.
Silver - Sorry to hear that. But Wow! I think you still look pretty young.
Is the conversation natural?
See above.
In your opening sentence, make it clear that she moved back to the US permanently. Using "went back"
could be taken to mean that she simply visited the US a few years ago. I added the potential "still", and "even though" because it adds context. It would add even more context if you gave us a bit more history, such as "Carol and I became friends in China [number] years ago and, even though she moved back to the US a few years ago, we're still friends."
In your second sentence, I'd say "we text each other", rather than the more convoluted "we send text messages to each other".
You don't need "come back" and "again". Saying "come back" makes it clear that something would be happening for at least the second time.
Carol's "I'm getting older and" isn't natural. Everyone's getting older. She might say "I think I'm too old to travel now" or something similar but simply stating her age is probably enough to get the message across.
Don't say "Sorry to hear that" when someone tells you their age! It's used when you hear someone else's bad news, such as the death of their relative or that they lost the job they loved.
A common phrase when you think someone looks younger than they've just told you they are is "You don't look it!", so you could say "78! Wow! You really don't look it."
