Do I use epoxy or CA for gluing the fin and stab to the fuse?

Properly done either will suffice. I find it much easier to use slow epoxy (at least 30 minute) as this give me time to be sure everything is properly alighned. Mostly though I use alphatic resin (Titebond II) as it is just as strong and much easier to handle.

I use slow epoxy for the same reason as Rodney

I use 5 min epoxy for that. Make sure you cut the covering off where the stab touches the fuse. glue won't stick to the covering and your tail will come off. If you use slower epoxy, make sure you pin it well in the correct position so it doesn't move on you while the glue is setting. Probably wouldn't use CA. You want to make sure you get a good joint on the first bird.

I like to use 30 min epoxy. Once everything is lined up put a drop of CA in a few vital spots and hit it with accelerator to lock it into position. That way you don't move anything while pinning. No pins needed.

Thats the way I would do it too, just figured that the risk of him locking it in the wrong place with instant glue was higher. That way is easier though.

I use Epoxy (30Min.) my experience with CA is that it has poor shear strength although I have not tried some of the newer more flexible CAs. I have an allergy to CA and only use it with much ventilation and only for CA hinges. Do my building with alaphetic resin.