Because they love the psychological effect, and they love to blow the crap out of everything they don't actually need. Overpowering force is the Dalek infantry way.
I've been thinking that "The Last Day" is the first time we've seen non-Time Lord Gallifreyans since "The Invasion of Time." The officer corps during the Time Wars was probably all Time Lords, but the cannon fodder in the trenches, like our POV character (and the noncom we saw at the start), was probably predominately Shobogans and other non-Timeys.
Actually thats wrong, we saw the 2 Gallifreyan technicians in the repair shop in 'The Name of the Doctor"
They could probably make a quicker way to exterminate people, but they really seem to love shooting one person at a time and in a way that seems incredibly painful. Daleks are just assholes.
Each Dalek has basically one MO, exterminate all non Dalek life in the universe. So sure maybe one Dalek would have been enough, but all the others were thinking exterminate, exterminate. Not "it's ok another Dalek is exterminating non Dalek life. We can do something esle."
Not really. The new series hasn't really gone too much into Gallifrey and its society structure. The classic era made it clear that not all Gallifreyans are Time Lords and the new series has done nothing to contradict that.
Last of the timelords seems to be too much of an integral part of the series to go back on. Same as how he was "on the run in a stolen Tardis" before. It's part of what makes the character interesting and vulnerable.
I always presumed Time Lords where the politicians, professors, doctors, commissioned officers and other top people while everyone else plain GallifrRyan.