I’ll give it a shot! Do I have access to the download links still or would I need to buy access again?
If you bought the game using this account, then you should be able to find the download link both on the store page and in your game library here. By logging into your account in the Itch launcher app you should be able to download the game through the app as well. If you bought the game without an Itch account, then you still used an email address and was sent a download link you can still access, and have it resent if you lost the email (https://itch.io/docs/buying/already-bought)
Either way you don't need to buy the game again :)
I suppose that is up to you. We can't really get involved in the refunding process unless Itch support reaches out to us first. If you did get it to work through the steps I mentioned and want to keep access to downloading the game, but you still get it refunded because of the initial refund request, then I'm guessing you'd have to buy it again if you want to keep the game (which could be nice if you're interested in downloading it again later, or if you want access to the big upcoming update we have scheduled for June).