@AB1, nice solutions. For #4, it turns out that even if repeat numbers were valid, there still wouldn’t be a solution. Can you find out why?
@Rhydwen23, I have that any magic square of primes can only consist of numbers that are either all 1 more than a multiple of 6 or all 1 less than a multiple of 6. Because of this I claim that the smallest solution that satisfies your conditions is:
31 73 7