No. The white marking gene that a flashy Boxer possesses is the same regardless of the colors of its parents. A flashy dog from a white x plain breeding is no more or less likely to produce white puppies than a flashy dog from a flashy x flashy or flashy x plain breeding. There is nothing magical that happens to the white marking gene when a dog has two copies of it; it acts exactly the same as it has for well over a century.

It is possible, in fact, that overall we’d see fewer white puppies, since breeders who breed flashy x flashy now, with a chance of 25% white puppies, might instead breed white x plain, leading to a 0% chance of white puppies.

No. Many breeders have a preference for plain dogs, and will continue to breed accordingly. Breeders who want to avoid producing white puppies will require a plain dog in every breeding pair. Plains are likely to become more desirable, in fact, as they will be necessary for any pairing that includes a white Boxer.

No more than we already are. The white marking gene (Sw) determines whether a dog will have white markings, and in very general terms how much (no copies = plain Boxer, very little white; one copy = flashy Boxer, generally up to 1/3 white; two copies = white Boxer, all or mostly white), but within those parameters the amount of markings is controlled by modifiers (much like the degree of brindling, or the depth of fawn color). These modifiers are not yet identified genetically, and there are likely multiple genes involved, but they in general control where pigment is present in the dog’s coat. “High white” modifiers (not an official term) block the migration of pigment (remember, white is a lack of pigment in the fur), while “low white” modifiers allow pigment to migrate. The late geneticist and Boxer breeder, Dr. Bruce Cattanach, discusses this in his “Dalmatian Dilemma” paper:

Studies in laboratory mice have shown that the pigment cells derive from the neural crest of the foetus.  Prior to birth, they migrate from this tissue and colonize pairs of specific sites on each side of the head and the backline of the body.  Three pairs of sites exist on the head.  One site lies close to the eye, another lies close to the ear, and a third lies at the occiput, the latter no doubt being the basis of the Blenheim spot of Cavaliers King Charles Spaniels.

Various estimates suggest that there are about six sites along each side of the body, with a possible larger number along the tail (Schaible 1969; Mintz and Russell 1967; Cattanach 1974).  At each site one or a very few pigment cells (maybe up to three, Lyon 1970) proliferate to give clones of cells which migrate outwards so that they join up, but they also spread down each side of the head and body until they meet up on the underside,  and further spread down the legs towards the toes.  The most remote regions (under the chin, chest, belly and lower limbs) are the most at risk of remaining uncolonised by the pigment cells and therefore white.  This is the most common basis of the white markings seen in many species, dogs, cats, mice, horses, cattle etc.

These modifier genes are the reason some flashy Boxers have a full collar, stockings, and wishbones, while others only have a small mark on the back of their neck, white feet, and little or no white on their face (and all the variations in between). They are already present in our Boxers, whether they are flashy, plain, or white. If a breeder gets mismarked flashy dogs in their litters, they will likely get mismarked flashy dogs when breeding a white to a plain. Generally speaking, breeders tend to breed away from excessive white markings, so we don’t see them with any unusual frequency, and there’s no reason to think we would if whites were included in breeding programs. The genes are already there — white Boxers aren’t bringing anything new.

In a word, No. The black mask is a fixed trait in Boxers; the only way to lose it would be to bring in a different breed that doesn’t have the gene for black mask (Em). White Boxers do have black masks, as can be seen in dogs that have colored patches on their faces (especially around the eyes).

If they do, there’s another breed in the mix. The Boxer does not carry the gene for progressive graying (fading coat color), and there is no evidence of coat color fading in Boxers of any color or marking pattern. (As Boxers get older they do get grey hairs, of course, which can make the coat color look lighter overall.) This Boxer puppy developed grey hairs in her senior years, but her colored areas are still well-pigmented.

No, albinism is something entirely different. White Boxers still have pigment, it’s just been blocked from spreading in most areas. We know that the white markings in Boxers are due to the Sw gene — this has been proven scientifically — which is not related to albinism. 

Absolutely not. The Boxer does not possess the gene for a solid black coat color. (While black Boxers appeared briefly in German in the 1920s, they were the descendants of a Schnauzer-Bulldog cross, and the color quickly went extinct after it was made a disqualification in 1925.) White markings have been part of the Boxer breed before it was formally a breed, since the influx of English Bulldogs in the 1830s.

No. One theory for the original disqualification of dogs with more than 1/3 white markings is that they would possess more of the “undesirable” Bulldog traits. (The other, mor common, theory being that white markings were too visible for nighttime guard and war work.) While that might have been a plausible theory a century ago, today we know that structurally white Boxers have the same range of quality as colored Boxers. After all, two Platinum Grand Champion Top Twenty flashy Boxers could produce a white puppy — does anyone really think that puppy will be of a lesser quality?

      
Can you tell which puppy has a white parent?

Yes, and no. Breeding plain Boxers of excellent type is more likely to produce puppies of excellent type, while breeding plain Boxers of poor type is more likely to produce puppies of poor type. There are no known links between color or marking pattern genes and structural/quality genes in Boxers; good parents will produce good puppies.