I will do the focus on the cat's colors, because this seems to be well known by breeders. (If I have more time, I would add some about the other attributes, but everyone is invited to do so, too ;) )
I found an interesting website with a lots of rules of thumb about the colors and pattern of cats. The most statements seem useful to me (I had some genetics in the studies).
But first, some essentials about genetics:
Each cat (each animal, each creature) has genes. There are so much of them, they need to be stored in some order, so the bodies are tidy and not a mess. They are stored in boxes, called chromosomes. Good for stacking and most times no problems with mixing contents. And they do not need much space.
These chromosome boxes exist in pairs. This is useful for diversity and to have some kind of plan B, if one box is lost, spilled or destroyed in any way. In cats (and other creatures, reproducing by mating) one box of each pair is from dad, and the other box from mum.
All boxes have the same amount of genes like their paired box. Except of one: the gender specific boxes, called X and Y. The Y box has less information than the X box (you can see, that the letter "Y" has one limb less than the letter "X", this was the reason to name this boxes X and Y - not a joke). Each male cat will have one X and one Y box, each female has two X boxes.
(And if you think about it now, you will see, that the male "decides" if the kittens will be male or female, by providing either his Y or his X box to them)
The color of a cat seems to be stored in this gender specific box pair, but in the X boxes only.
The Basic Feline Genetics for example states (while dam is the female parent and sire is the male parent):
Male kittens always obtain both color genes from the dam. The male offspring in a litter will always be either the color of the dam (or one of the colors in the case of parti-colors) or the dilute form of the dam’s color. See the statement on dilutes for more information (see #21 & #24).
Female kittens take one color gene from each parent. The color of the female kittens in a litter will always be either a combination of the sire’s and dam’s colors, or the dilute form of those colors (see #21 & #24).
Because the color is stored in the gender specific X boxes only, the male parent can provide it only with his X box to the female kittens (X from mum, X from dad) and not in the Y box to his male kittens (X from mum, Y from dad). Then all male kittens will have the color from mum only, while the female kittens will have some kind of mix of mum's and dad's color.
To obtain any of the red or cream color/patterns in female kittens, the sire must be one of the red or cream color/patterns PLUS the dam must in some form demonstrate red or cream (see #21).
Only the immediate parents determine the color/pattern of a kitten. The color/patterns found in the pedigree of a kitten will NOT always directly affect the color/pattern of the kitten. One notable exception is the colorpoint gene, which can carry through a number of generations (see #21 & #24).
Sounds logical: the kittens get their chromosome-boxes from the parents, not from the grandparents. And because the color is stored in the X box only, there is only one color in the male parent, which cannot hide in any kind.
- A kitten’s pattern can be inherited from either parent.
The pattern then is stored in each of the two boxes of it's chromosome pair. This could be the doubled information of X and Y, but also any other pair of chromosome-boxes.
A dominant characteristic (all dominant colors and patterns such as shaded, smoke, white, tabby, bi-color, etc.) cannot skip generations. The characteristic cannot be transmitted from one generation to the next without showing that characteristic in each generation.
A cat displaying a dominant color (black, red, tortie, etc.) must have a parent which displays a dominant color (see #21).
If there are two boxes with the same kind of information (not the same information itself, but describing the same attribute), then we need some rule to know, which of this two instances of information will be used in "producing" the kitten. There are two kinds of genes: dominant and recessive. As the names say, a box containing dominant information will rule out another box with recessive information. Now we know, that shaded, smoke, white, tabby, bi-color, black, red, tortie and others are dominant information. Only recessive information can hide (while ruled out by a dominant one), so dominant attributes cannot skip a generation.
- Two recessive color parents (cream, blue, etc.) cannot produce an offspring of a dominant color (black, red, etc.).
Logical, because the recessive color can only be shown in absence of any dominant color - no dominant box to provide the kitten.
The next rules take focus to special colors and patterns, like colorpoint and smoke, so I will skip them.
- A bi-color must have a bi-color parent (see #21).
This sounds like the gene for bi-color is not recessive (remember: recessive genes could hide for one generation, if ruled out by a dominant gene).
Points referenced before:
- Genetics for solid white cats can affect the possible color/pattern of expected kittens in that the white parent may be masking the color/pattern needed to produce this result.
White seems to be an additional gene, "deleting" all color information. So there is a good chance, that the mum may hide some additional color under their white parts of fur (I am not sure, if this need to be the second (black) from the bi-color or could be some surprising third color). That additional color she could give to the kittens
- The dilute gene must be present in both the sire and dam’s pedigree in order to produce a dilute offspring.
This means, the dilution gene is a recessive gene, and only if mum AND dad have one (could be hidden) and both give it to the kitten, the kitten would have a diluted color (means for example blue or cream)
With the information about color and pattern you provided: mum is bi-color black and white, and dad is gray (which I will interpret as "blue" - means diluted black, if he is tabby, then the conclusions will not work, and you need to let me know).
Then you have good chances, that the male kittens are black, blue or white (happy you, that the mum provides two colors), while the female kittens get an additional portion of black from dad.
Some of the kittens will get the recessive "dilute" gene from the dad, but the belonging gene from the mum will decide, if the dilution will hide (mum's dominant gene rules dilution out) or not (mum has a hiding, recessive dilution gene too). Also the dilution could be combined with another color, provided by the mum. But white (her second color beneath black) will not be affected by it.
So the most probable in female kittens would be some of this three: black/blue/bi-color-with-black. A female pure white cat is less probable. In males there will be the equal possibility for black and white. Some of the black ones could have the diluted gene, then being blue. And some of the kittens will get the bi-color gene from the mum, then combining white with black or blue, or even combine mum's black with dad's black and be bi-color without showing it. If the mum hides some additional color, this will only show in a male kitten.
(Another interesting (but here not used) source: Cat coat genetics at Wikipedia .)
Addendum: After reading the linked article at Wikipedia, The fur length seems to depend only on one gene. The long hair is here described as recessive gene, while the short hair is dominant. If your cats are both pure breed in their fur length (means mum has two boxes with dominant short hair attribute and dad has two boxes with recessive long hair attribute) then all kittens would have short hair (because getting one dominant short hair from mum which would rule dad's recessive long hair out). Dad need to have two recessive long hair genes to get a real long hair fur. So the only way to get long hair kittens would be, that mum hides a recessive long hair gene behind her dominant short hair gene.