Where can I get F-Droid swag (shirts, hoodies, stickers, stuff and so on)?
At your local print shop.
Regarding my local print shop: Do you have special designs that I could give them?
Did you find some special ressources for copy shops there? I just see the logo and the badges.
It has the “official” F-Droid artwork, which should be suitable for turning into any copy shop material you’d like. I’m not aware of anything ready-made specifically for copy shops, but maybe someone else knows more.