If you do the second ending and get the RED PLANE artifact you can skip world 3 missions.
And the purple slime key place is called Plasma Hole
And that last place is called "HAPPY ZONE"
Someone’s baking a pie in the house. Is there any way to ask the man who’s baking a pie come to happy party ? Or the happy party is vacant .
Nope, there is no way.
I'm pretty sure Happy Party Enterance is a tease at the dev's next game, which is also called Happy Party, i'm assuming that interacting with the MACHINE in that area will bring you to the page for Happy Party in a future update.