Can the plaintiff send the summons for a Minnesota small claims court case via certified, but not signed, mail to the defendant's father's house and write a note asking defendant's father to give the summons to the defendant? Does this constitute being served?

Only if the court accepts it, is the defendants father house a known residence for the defendant. Was it given to the defendant.

The signing of the certified mail is the service, the issue is if the defendant lives there or is known to have lived there.

Mailing a summons by certified mail normally requires that the receipt be signed by the addressee (the defendant) only. It is possible for the defendant to sign a form with the post office authorizing others to accept his "addressee only" mail, and this also could work. But it doesn't appear that what you describe fits the bill.