Hey kradarak,
you need a rope and an ashwood stick to craft the fishing rod. I would agree, that they should add a finished fishing rod item, that u can loot somewhere.
You can get filets out of the fish, if you put the carp out of your inventory to the ground. If u have a knife you can select "skin and quarter the body", after that u will get the filets and the guts in your inventory.
I also ran into that bug, and theres already a reported issue about it. But also the devs couldnt reproduce this, cause they closed two reports about this. Sometimes I dont know what they are doing.