RE: can you repair carbon arrows
While I certainly wouldn't consider myself a rich man, and arrows are not exactally cheap, I wouldn't even think of using an arrow I suspected of being cracked, much less one that has visible cracks. Even after being cut down, you have put a tremendous stress on the fibers and the epoxy that holds them together. Cut it off and use it for a decoy stake or to hold up your tomato plants. Or you could cut it way down to like 8", fletch it up and make a pen. That's what I do with my broken ones.
BTW: My nephews think the arrow pens are just the coolest things.