Can this be used in a "no more/i've had enough" sort of way? (i.e: like when full at a restaurant). Or is this only to be used to state something is "correct"?
Can the phrases you mention also be used in an "I can't take this any more /stop bothering me!" kind of way -- as when a child has been misbehaving for what seems like forever, or someone you're not the least bit interested in keeps pestering you to go out on a date?
Well, to use it for that purpose, it should match the gender of the object. As it stands, "To je ono" works for neuter objects. In your jacket example, you'd use "To je ona!" for "That's the one!", and for masculine objects "To je on!"