It's been said that B and Jaid nibble on the cat food when they are out and walking around. Everyday they come out they crunch a niblet. I don't know if they eat it or if they just break it into a million pieces, but could that mean they are lacking protein and seeking it from another source?

It's hard to say. They might be seeking out some nutrient that they need more of. Or they might just enjoy the taste and/or texture. Or they enjoy foraging.

Is it a problem if the kibble has been in cat's mouth and has saliva on it?

I hadn't thought of that. It could definitely be a problem if the cat has been munching on the same kibble and the birds are taking their kibble out of the cat's dish. Cat saliva has bacteria in it that's very dangerous to birds.