"When purchasing insurance for mailing a package, does it guarantee it will arrive at the addressee or does it guarantee it will arrive in its original condition?"

USPS does not guarantee anything. That's why they offer insurance. In the event an insured package is lost or damaged the sender can file an insurance claim with documentation as to value claimed.

"If a package that is not insured or have delivery confirmation, there is really no way of knowing if the sender actually sent the item, right?"

That's correct Larry. In other words, there is no record of a package being shipped if it was mailed uninsured or no delivery confirmation service having been paid for.