How do I play the game?

Check out this quick tutorial. Hopefully, it will help you get started.
Quick Tutorial (Opens in new tab)

Are there items for sale in Polytopia?

Yes, you can buy additional content in the form of more tribes or skins for the tribes. All products are of the kind that you buy once and keep forever.

Can Polytopia be played without making any in-app purchases?

Yes.
The mobile version of the game can be played without making any in-app purchases, but you have to make a purchase to access online multiplayer.
The PC version requires no additional purchase apart from the base game.

Are purchases refundable?

Yes, https://www.epicgames.com/site/en-US/store-refund-policy (Opens in new tab)

What payment platform is used to facilitate these purchases?

Purchases are made through the Epic Games Store platform