For example, how fast can a new species arise from the existing stock of
species? BRBR

It varies widely. Apparently for humans & other primates it took millions of
years. For orchids & some other plants which colonize a newly disturbed site in
the jungle, it may only take a few generations.

What are the mechanisms that effect the event?

Sorry, that can not be explained in a short e-mail. You need to consult a few
books on the subject, starting with the Origin of Species.

Is natural law but a subset of a Creator?

Maybe. Consult your clergyman.

Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)