A: Shield mitigation blocks a certain % of damage received to shields (sort of like an armor value for shields). The base value is 20%, but it can increase up to 59% when being hit many times in a short period of time.
Shield mitigation increases when a ship is being shot at. The more its being shot at, the higher is its shield mitigation (to a cap of course, think its 57% base for normal ships and 65% for caps). Advent get techs that increases mitigation, both overall and when they are in their own culture.
Someone fires at you with a weapon that "would" do 3.0 damage, but you have 50% shield mitigation, so it does 50% damage.
There must be some sort of level guage for the mitigation levels, so says - Okay, after you've taken a cumulative set of 500.0 hp damage points to your shield, increase mitigation by 6% or something - Advent at least have a few sheild mit' skills that I've seen, highest I've ever got a capital ship to was 59%...
But to answer your question, the damage mitigation would only affect the shield - Once they penetrated the shield it would be full damage again.