How is it right to say in the yard or on the yard?

Answer 1

Either one is fine. (If you were raised speaking English, anything that sounds natural to you is right. The dictionary authors aren't in control of the language - the speakers are.)

Answer 2

The correct preposition to use depends on the specific context. "In the yard" typically refers to being inside the boundaries of the yard, while "on the yard" would suggest being on the surface of the yard. For example, you would say "in the yard" if you were playing within the yard's confines, and "on the yard" if you were standing on top of it.