You have a good question. The answer is yes, there are many possible combinations of the five main rabbit color genes, as well as a variety of pattern genes (like spotted/broken) and modifiers (like the rufus modifier and wide-band that makes the New Zealand Red such a rich red. Any rabbit can have any of those combinations, but the 'powers that be', like the American Rabbit Breeders Association in conjunction with the individual national breed organizations, decide what colors/patterns are going to be 'legal' within that breed.
If there are not enough entries in a color category, they may decide to drop that color as an acceptable color for show/registry. If there is enough interest, someone may be granted a Certificate of Development (COD) to develop and show a new color, with a strict and lengthy process to be followed. So acceptable colors do change with time.
Anyone can have recessive genetics or certain gene combinations cause unshowable colors in the nestbox. They are still 'purebred', but neither showable nor registerable. For instance, in my breed, chinchilla is an accepted color. Fawn is an accepted color. But if I cross a chinchilla with a fawn, I am likely to come up with ermines, where the chinchilla gene eliminates the fawn coloration, leaving only a steel gray-eyed pearly white rabbit with a few colored marks on the face and ears where the 'smut' would have been on a fawn. Ermines are not accepted for show. The stock is all purebred, but this color is not acceptable for show.
Some breeds have dozens of accepted colors, others just one. The genetics for the other colors may all still be there, but only those in the sanctioned colors can be shown or registered. If you buy stock from breeders that still breed the unshowable colors in their herd, you too, are likely to end up with unshowable stock. If showing is your goal, you want to purchase stock from breeders that limit themselves to accepted colors, otherwise, many of the kits in the nestbox may not be showable material.
There is a page at
Agouti Group (A-) [Mink Hollow Rabbitry] that shows some of these colors. Amber, also called chocolate agouti in some breeds, is illustrated there. It looks to me like it's possible someone bred a NZ white or black with a NZ red. The reds have the agouti gene, coded
A with a capital letter because it is dominant, and you only need one copy of it for the rabbit to look agouti. Instead of being one solid color, agouti puts multiple colors on one hairshaft, plus the light eyerings, belly an around the nose, as your rabbits have. The reds also have the double recessive yellow (fawn) gene, coded
ee, which pulls the center fawn agouti band out to the tip of the hairshaft, and a red (
rufus) modifier that turns the yellow/orange fawn band to that lovely rich red. However, black does not need that fawn recessive, the rufus modifier, nor does it have agouti. White could be anything genetically, it can be any color combination, but the double recessive albino gene, coded
cc, stops the rabbit's pigment factories from making any color, so its genetics are hiding under an albino white sheet.
If you cross an agouti (which a NZ red is) with any other rabbit, you are likely to get more agouti rabbits, as it is dominant. It takes two recessive fawn genes, two recessive wide-band genes, and rufus modifiers to make red rabbits. If you breed a NZ red to a rabbit that does not carry these recessive genetics, the offspring will not have them. The most likely result of this cross is a chestnut agouti, a black agouti (born black, the chestnut coloring grows in as the hair grows). Amber is the chocolate recessive of black, born chocolate, the chestnut coloring also grows in as the hair grows, but with a chocolate base it has a different look. Another possibility is that the bunny is wide-band recessive, making the final coat look more fawn, without having the actual double recessive
ee genetics.
The size issue is a whole 'nother issue. While it may be a red flag along with the color that crossing has occurred, you may also have the result of illness, parasites, a runt, poor milk production from the dam (or too many kits in the litter for the available milk), poor eating after weaning resulting in poor growth, low-nutrition feed, poor genetics. . .the list could go on. Six months old is 'adult' in many breeds, so if the given age was correct, she was only half accepted weight.
It looks like some of the feed manufacturers are suggesting 4-6 oz. of 18% protein pellets for a New Zealand doe per day, you'd need to weigh your brand and see how much that would be, there should be rabbit weight suggestions for feeding. The pet websites are suggesting that amount of fresh greens instead, and a tiny amount of pellets, which doesn't sustain growth well, especially on rabbits not bred for that type of feeding. Yes, you can raise meat rabbits on greens alone, but it may take you several generations to come up with a line that does well on that kind of diet. I'm a real fan of 'breed to the feed', where you select those rabbits that grow well and are healthy on the feed that is available to you. That takes time, and you're starting out with an original generation. It sounds like your doe wasn't doing as well on the system in her previous home weight-wise, but is doing better under your care. Good job!