Is it permissible to eat from a food sample offered willingly by the shop owner for promotional purposes, and is it obligatory to pay its value if it was eaten previously?

It is permissible to taste food when purchasing it, especially if the seller grants permission. There is no harm in doing so at the time of purchase. However, for someone who does not intend to buy, it is not permissible to taste the food without the owner's permission. Therefore, as long as you tasted the foods with the permission of their owners, given willingly by them, there is no sin upon you, and you are not required to return anything from that.