correct or incorrect?

English as a Second Language English Vocabulary, Grammar and Idioms
1
  1. He wished her son pass the exam.
  2. He wished her son a pass the exam.
    Are the above two sentence correct?
2

He wished that her son would pass the exam.
He wished her son a pass in the exam.

3

Can I write these?
He wished that her son might pass the exam.

4

You can write these:

He wished/hoped (that) her son would pass the exam.
He wished her son a pass in the exam.-- This is BrE; in AmE we don’t use ‘pass’ as a noun as here.
He wished/hoped (that) her son might pass the exam.

5

Here that is optional. correct?

6

Yes.