All of my answers are now being compressed into this post to help with confusion. :3
What book series are these from?
These dragons are based of the Age of Fire Series written by E. E. Knight, the website for the books can be found
here. Keep in mind that the website hasn't been updated in quite a while. It's a six-book series and the sixth and final book comes out this December.
How do you get these?
Whenever you adopt ANY Malk Pet, it has the chance of being a dragon egg instead of the other Malk newborn, but only if a new dragon has been made. So all of the dragons are currently retired and you currently have NO CHANCE of getting a dragon egg. Next month, however, if Malk makes a new dragon color, there will be another chance to adopt a dragon. (Each dragon had one month of being released before being retired for good.) The chance of you adopting a Malk Dragon is a small percentage (I'm not sure of the exact number.) This applies to the red, white, and blue Malk dragons.
The gray, green, and copper Malk Dragons were released in October of 2009 and everybody could adopt an egg - they are also no longer available.
The white dragon was released twice - once by itself and once with the red dragon.
Rarities?
All of the rarities in Malk's post are not according to the CS rarities, but the rarities in the book.
In the book, there are eight colors of scales for male dragons: copper, bronze, blue, red, black, silver, gold, and white. There are also rare gray dragons who have no scales. The rarest is the gray, of course, and white dragons are also fairly rare. Most of the other colors are considered to be fairly common.
Female dragons are nearly always green, and easy to find - making them very common. Male dragons usually die in nest fights, so females highly outpopulate the males.
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According to the CS rarites, most of the "UR" dragons are more rare than the gray. The order of CS rarities is listed below from most rare to least rare:
Blue Dragon | White Dragon | Gray Dragon | Red Dragon | Copper Dragon | Green Dragon

Started out Very Rare.

Started out Very Rare.

Started out Rare, changed to Very Rare.

Started out Rare, changed to Very Rare.

Started out Uncommon, has yet to change.

Started out Common, changed to Uncommon.