Is it right to say "Thank you" in the response of "Thank you"?

I personally would respond with "No, thank you" or "thank you." That is, there's an emphasis that I consider the other person to have been of equal or greater help. (American English)

Sounds good to me. You could also say "You, too" or "Thank you, too" or "Ditto" or anything equivalent.

mkennedy and Hackworth are right, but one might also say "and thank you for the [blah blah blah]". If one parrots "thank you" then it is possible that one's gratitude might sound hollow, so adding detail of what you are grateful for might make the utterance sound more genuine.

I thought that the person who receive the "Thank you" will say "You're welcome".

In your example: Jack and I have helped each other. Then Jack will say "Thank you" to me and I will say "You're welcome." After that, I will say "Thank you" to Jack and Jack will say "You're welcome too".