I heard that there is a big Shailah if a father can promise his child that he will buy him a toy or give him some money if he returns the Afikomen. Is that correct?

Firstly one must say as usual that it is all B’li Neder. The recently published Kuntres Moadei Shlomo (p. 72), quotes Horav Shlomo Miller’s Shlit’a opinion that one should avoid using the term ‘buying’ which one may not do during Yom Tov but rather just giving. He adds that although money is ‘Muktza’ it is permitted to just say that he will give him that money since the child may accept a gift given instead.