I want to make a memory quilt for my son. Should I wash the quilt [after finished] to fray, then iron on the pictures of his son and him?

depends on how you are printing the pictures- what you are using- will they be transfers (like ironed onto t-shirts? or are you printing pictures onto fabric?
will the pictures be washable?
you do need to wash/dry the quilt to fray the edges-
there are a number of different techniques/products for adding pictures- it depends on what you are using how and when the pics should be added

the pictures will be printed on the sheets you buy then ironed on.