Can I go to Yucheng Primary School without going to kindergarten in Yucheng?

Of course. Kindergarten and primary school are not in the same city. Kindergartens can be public or private. If it is public, you must have a household registration book, real estate license, or temporary residence permit, and you must attend primary school in the school district. If they are private, they must take the exam before school starts. If it is qualified, it will not be accepted.