Patch Eye Pim might only respond to you if an annoying person is in your party.
I'm already giving you many hints XD
Unfortunately, the Demo does not have a 'perfect' clear and you cannot bring over your accumulated stats to a new game.
What the demo can do, however, is reward you with interesting and different treasures from chests on every new playthrough.
In the full game, you can carry over all your equipment and stats when you obtain/unlock a game clear, a special ending or a slave ending.
I'm really glad you enjoyed the game :)