In reply to "Thank you"

In reply to "Thank you!":

Americans prefer "You are welcome."
The British prefers "Not at all.", "Don't mention it."

Instead of saying the above, can we say "No problem.","Thank you.",
or just give a smile back without saying anything?

I read a travel story written by a Chinese talking about his tour in Australia. He was impressed that each time he thanked an Aussie for
any help or kindness, he got a "Thank you" back. He was very much amused by this, "Who should thank whom?"

:) Thanks!

[Red5]

I think it depends on how formal the situation is.

"Not at all" or "Don't mention it" are both okay for formal occasions, but we British also would use "You're welcome".

A reply like "No problem" is very much less formal, in my opinion.

I hope this helps.

Yes, it is much more informal. - "No problem."

Don't forget about "My pleasure."

That's very polite sounding. I would use it in a formal circumstance.