[Trombone12]

a) Well, according to a review paper from 2011, it has an effective aperture that is about twice that of the Arecibo telescope, can see three times the amount of sky that Arecibo can, and has 30 % better spatial resolution. The larger aperture and newer design probably accounts for the fact that it is predicted to have three times the raw sensitivity of Arecibo, and the design of placing just a reflector on the wires instead of the entire receiver is probably the cause for the 10 times faster surveying speed.

The raw sensitivity alone means that it will roughly speaking accomplish three times the science per time unit as Arecibo.

b) One is a gigantic dish and the other is a bunch of big dishes. Correctly arranged the bunch of big dishes can emulate a very very big dish in the resolution sense, but not at all with the same sensitivity as the very very big dish they emulate. The advantage with a gigantic dish is that you get high sensitivity, so science can happen faster. The advantage with a bunch of big dishes is that they are much cheaper than the very very big dish they can emulate.

c) Waves from the normal go to one focus, waves from directions away from the normal go somewhere else. So you simply put your detector in the focus corresponding to the direction you want to look at. The FAST also has an ability to deform the main dish to help with this directionality.