For the first, you want to get a slime slab from the green slime dragons in the cave. You can do that by letting them grapple you to completion when you have more than 50 STM, and then using the nearby fire...
Take the slime slab back to the wizard at the inn, ask about "oddity", there'll be a scene... and then the slime cast will appear at the blacksmith's place. Interact with it... and the scene will play out.
The second one requires having 10 or more Corruption. You can raise this by getting slimesuited by the slime dragons, just make sure to recover after each one.
Once you have that amount... go to the campsite to the west / left of the inn, and try repeatedly to enter the tent...!