what are the rules for children being born with parents from two different races??

Well normally my posts would contain some kind of story... but well... the question says all...

Have a http://www.imperial-library.info/content/morrowind-notes-racial-phylogeny-and-biology

For the lazy, the offspring's race is determined by the mom's race. There are bits of dad, but it's very subtle, the person is 100% of the race of the mom for all intents and purposes.

Also, the Grey Prince was special, because his dad was a vampire, which changes things.

I've always wondered, does this have the same affect if they're from closely related races? For example a Dunmer women and a Nordic father = Dunmer kid. But what about a Nordic father and a Nibenean wife?

It'll be a Niben for all intents and purposes.

Thats...tricky. "Closely related" races are often more a cultural distinction than a biological one. If the Nibenean mother is of pure Nedic stock, her child will probably look more Nibenean than Nordic (darker, shorter). But, given that Cyrodiil is already a jumble of both Nedic and Nordic blood, he would probably come out looking like your average brunette European type.

On this question in regards to Khajiit. . .

Mommy Khajiit + Daddy non-Khajiit -> The "breed" of Khajiit of the offspring is still determined by the lunar phase correct?

Second Q, if two of the smaller varieties of Khajiit mate, they can still have an offspring that turns out to be one of those huge Khajiit used as mounts. This must be hell on the mother giving birth right? There must be a high rate of maternal death during birth. Or do the kittens generally the same size when they are born regardless of "breed?"

Khajiit children and babies start off as kittens, so there is no tiger sized kitten made by a house cat. This was supported in the TES book. My guess is that once adolescence hit, they morph into their moon phase form, like with most life forms.

And, in theory, yes the baby would be a khajiit, and like with all khajiit, it's form depends on the moon phase. Of course, it's up in the air whether khajiit can breed with other races. However, they have a lineage with the mer, so it's possible. With argonians, they're a completely separate line from men and mer, not to mention have a much different biology, so they're a no no with anyone else.

Of course, you can still have six with both.