From what I´ve read, the slobbering has a lot to do with anxiety.
The more anxious they are, the more slobber you get. You can reduce the anxiety if you feed always at the same hours, take them out for a walk several times (3 to 4 in our case) a day, etc
But, as always with animals, it depends a lot on the individual as well.
As regards the white boxers, its just a recessive gene present in all boxers that have some white in their body (even if just a spot). Two brown parents - as long as one of them has the recessive gene - may have only white puppies (of course, the albinos are a different story)
They used to euthenize the white boxers (some breeders still do) because according to the (very old...from way before they found out why some dogs were born white) internacional standards if more than 1/3 of the body is white, they are "out of pattern" and thus not considered pure...
Things are changing now, because a few years ago, they crossed the Canadian and All America champions and 6 out of 8 puppies were... totally white. Shocking !!

.
I believe in the US they´re now talking seriously about changing this pattern issue (they were, at least some time ago. Don´t know how things are at the moment).
So, nowadays, most breeder are allowing white puppies to live. Nevertheless, it was a bit difficult for us to find a white boxer (and we really wanted a white one)