ONE: The dark spots are called BER(Blossom End Rot). It is not a disease but a physiological disorder, relating to the uptake of calcium. Practically there is nothing anybody can do about it other than trying to be consistent in watering and maintaining soil moisture. The good news, perhaps, is that this situation will not last all season long and should end soon.

TWO: when to pick ? Easiest answer is that when they have nice ripened color. But Then there is danger of birds eating them, cracking etc. So I have read (here on GW) that you can pick tomatoes any time after color break and let them sit on the counter top in your kitchen(NO direct sun) until they become nice n red/yellow ,...