What is the number of influenza strains occurring at a given time?
Antigenic drift in the coding portions of the genes that involve antibody binding sites accounts for the seasonal variability of flu strains, i.e. they mutated enough that the antigens require new antibodies, hence a new strain. The process is as you said constant, like evolution, and in an analysis of pandemic H1N1 the authors are able to note 1 - 18.1 mutations per genome per replication cycle (ref). Because of this, flu vaccines tend to have more A strains than B strains due to the greater mutability of influenza A, at approx. 30% more mutations per site per infectious cycle (ref). At current It will take me time to research the remaining questions.

Interestingly enough, however, and I've never looked at this but CDC offers weekly influenza reports that detail by region what they're finding (CDC):



Source: CDC's so-called FluView

Beyond that, I'm pretty sure they take this weekly data, see what strain is on the rise in hospitals, and manufacture the vaccine to mirror the "popular" cocktail of strains.