are there rare coats for different monsters? (not counting deviant or if someone put a coat on)

http://beastkeeper.com/skin-lib -- Has all the skins for beasts, though I'm not too sure about Kamis.

If you're talking about the monsters on the islands, they typically only have 3 variations, though some don't have any. Don't have/know a link to send you to, though.

Relatively speaking, yes, but it just depends on the power of the genes and what people are breeding for.

Let's use Lykos as an example.  The Pearl color has the lowest frequency while Merle is the least common pattern. If the pet is born with any other color/pattern along with it then these 2 genes will be recessive and not show up in the pet.

We can test this, as it is simply a theory based on the mechanics of the game and the genes, by using the ajax search (which is a Premium feature). There are 54 Lykos with these two genes dominant, although the fault in the system is that it only takes into account pets who have these genes researched. If we search Brown + Normal Lykos, as these are the most frequent based on their power, we find that there are 538 Lykos with this particular coat. There are 14,278 total Lykos in the game and 30 possible skins.

We can try this for other species as well. The least common skin + pattern combo for Cockatrices, based on the genes and their powers, would be Silver + Striped while the most common would be Green + Normal. There are 62 Silver + Striped Cockatrices and 1,566 Green + Normal ones.

Hmm, ajax search... OK.