"What happens if my father drops the charges?"
*** Then MasterCard would very likely reinstate the debt against your father.
"(friend is agreeing to pay the bill off, we're sure he will and don't wish to prosecute)"
*** The right to prosecute or not once the charge is filed is not yours. It rests with the state or federal government (depending on charge).
"Or if the unauthorized use was traced to this family friend but he doesn't cooperate and drags this into court... we don't want that."
*** Sorry, but what you want may have little to do with this.
"We just want Mastercard to settle this, but they told my father to press charges."
*** What do you mean by having them 'settle this'??
One thing you need to understand, when there is an issue of fraud, there are two separate actions that could happen. The first is criminal charges. As noted above, the 'victim' may be called to testify as to the facts, but has no real issue to stop the proceedings. The other is civil liability for the action and the plaintiff (MasterCard in this case) can pursue collection of this debt through the courts.
"We would rather this friend get help (they have mental problems) and NOT go to prison. Our father is being uncooperative and is worried about Mastercard's policies. He wants to get this over with....and since the report was filed he cannot accept payment from the family friend. He seems to think this is too far along."
*** And since your father is the VICTIM here, his actions will be the only ones that matter. Personally, I agree with him..... the debt will be on him WHEN (not if) this 'friend' doesn't pay.
There are at least 17 lawsuits (!!) filed in various courts, including the US Supreme Court, asking if Obama is a natural born citizen (as req'd by Art II, Sec 1 of the US Constitution).
Why has he spent over $1.7M in legal fees to block disclosure... rather than spend $12 for a VALID birth cert to settle the matter? The 'certificate' he has presented doesn't qualify to get a drivers license, wouldn't allow a child to qualify for Little League, or for a real citizen to get a US passport!