Can Cats Eat Raw Salmon?

Yes, they can eat raw salmon, or any raw meat, just the same as if they were a feral cat and had to catch their food on their own. 
 
You can also try different brands of cat food as well.  Just because your cat doesn't like the one or ones you have tried so far, it may just be a matter of finding the right food.
 
And this will be expensive, but probably cheaper than buying raw meat for your cat, is your cat can also eat chicken or turkey baby food.  After our kitten had a reaction to injections last fall and we ended up in the pet ER with him, they told us to put him on a bland diet that night--the baby food. 

Be careful with raw fish, it contains parasites, mercury and other things that might be harmful, it's better to slightly cook fish, you can give raw chicken, chicken livers,gizzards (that's what my cats eat) but please no pork, go to www.max'shouse.com for a great site on cat nutrition, also Dr Lisa Pierson has a very informative site, I use her recipe for my cats, her address is www.catinfo.org good luck

Yes, but take the skin off. Very high fat content and they will have gas so bad that you won't be able to stay in the house.
A little bit goes a long way...