They shouldn't be excessively rare, you might have gotten bad luck. I realize farming can be a bit of a pain in this demo, but there will be systems to facilitate it in the next one.
No, the wrong code just summons a random enemy. Being able to summon a speific enemy in some way is a cool idea though, I'll keep that in mind!
The tea set can be completed! The plate and pot recipes are hidden, but the walkthrough can help you find them: https://www.patreon.com/posts/walkthrough-by-33962675