I found a shack with 3 sunset star caps, are those fake? Does it affect the star caps hunt thing?

No they do not. Any Sunset Sasaprilla Star caps you find are counted towards the 50 you need. The 'Counterfeit Bottle Caps', which are named as such, are set pieces and not capable to be used as currency.

Thanks.
Counterfeiting caps, thats funny.

It'd be a great way to make money for nothing. Too bad you can't make a different choice in the Pressing Matters subquest: feed in some Scrap Metal, and generate 100 bottlecaps.