cat claw problems/vomit issues

Question
My cats tend to fight every night with each other.  I noticed blood today and a missing back claw.  I don't know if I should just let nature run it's course, or if I should doctor it somehow.  These 2 cats are 5 and 7 and a father/son pair.  I got them from a lady who had them since they were little and had to get rid of them because of the dogs. I don't understand why they fight every night.  The other problem is that they (or maybe just one) pukes a lot.  It has no smell to it and it looks exactly like its food which is Purina Chow indoor formula.  This is what the last owner said she has always fed them.  I have never changed the food.  Some days there is no puke and some days I clean it up several times.  I don't understand why this keeps happening or what to do about this problem. Please help!  :)  

Answer
First things first, are these boys neutered? If so, we can move to the next possibility, but if not I can be 99% sure that they are fighting for territory.

Even if they are neutered, they could be fighting over territory. They could be fighting for the box, for a favorite sleeping place, or for food. Male cats are notorious for these things.

To help stop the fighting, I suggest the following:

-Get a second or third cat box, in case they are fighting over scent marking the box.
-Get a second set of food and water bowls.
-Get them separated when unsupervised.

As for the mild injury, I suggest you pour peroxide over the  area, wipe with a cotton ball, and repeat three more times. After that, make sure the area stays clean and you shouldn't have a problem with infection.

As for the vomiting, your cat is most likely eating too much, too fast, and/or not being brushed enough. With the weather changing, most cats are shedding a coat, and when they overeat or eat too fast, combined with the fur they ingest from cleaning, they can make themselves vomit.

I suggest having the cats eat from a very, very shallow, wide bowl, or better still, a plate. They will have to eat less, slower. Purina's indoor formula is a good choice for feeding.

Hope this helps!