Basics of frequency spectrum for onset detection using FFT
Here are some thoughts concerning your questions:


I guess you have to find the relevant frequency range by experiment, because, depending on the instrument, a lot of signal energy can be in the harmonics.
If your sampling frequency is 44.1 kHz and you use a 1024 point FFT your frequency interval is about 43 Hz, because the 513 points you mentioned are between DC and half the sampling frequency.
You could indeed average some frequency bins, or simply use a shorter FFT length.
I would say your methodology is pretty reasonable. Have you checked the literature? You're probably not the first one the do onset detection.