If to be a dragon is canceled by, say, Paper Shield, does the character chosen still stand? My thought is that it does, because standing the character is a cost. When a card effect like 'Seat of Power' is canceled, the cost is still expended (Discarding 'Seat of Power'). So, does the character stand?

You're right. Since standing a character is a cost, cancelling To Be a Dragon's effect won't prevent it.