If you or the giver hold the superstition, yes, and it takes two seconds. The tradition says a gifted blade cuts the friendship unless the recipient hands back a small coin, converting the gift into a symbolic purchase. Most knife people do it out of habit rather than belief.
The recipient offers the coin, not the giver. Many givers pre-empt it by taping a penny to the box, which is a friendly way of saying they know the tradition and you do not need to fumble for change.
Either version works. Neither is wrong.
No. It is folklore. Nobody will be offended if you do not, and a recipient who does not know the tradition is not committing a faux pas.
Among people who collect or work with knives it is common enough that going along with it is easier than explaining that you do not.
Hand back a coin the same day and say thank you properly. If you want to be charming about it, a coin from the year the knife was made, or from a year that means something to both of you.