That's great. Is there any charge or fee to pay if i do this?
Not at all. I you apply and were charged a document fee, then you're entitled to a refund for the fee you paid.
This proof i have to submit, it has something to do with it my discharge date?
Well, yeah. If your discharge happened before January 1, 1950, then you should submit a Honorable Discharge Form WD AGO 53, or WD AGO 55, or WD AGO 53-55, or just an "Enlisted Separation Paper"