Your car is to rights.
*I have no idea what this means.
The woman who came yesterday was on the right side of thirty.
*I am not familiar with this idiom. When I googled it, it looks like the idiom is "wrong side of [age]" and can't be changed to "right side".
You should set oneself right with your friends.
*You should set yourself right with your friends. [advice]
OR
*One should set oneself right with one's friends. [general principle]
My son is at the head of the class.
*Great job!