How can I identify when and where I need a repeater, and if my wireless throughput is consistently sufficient for lossless streaming?
I would suggest starting by checking out this AirPort User Tip. It should provide you with the basics to determine the best placement of your AirPorts in an extended network.
Next, you should arm yourself with some throughput measuring tools. One I would suggest is AJA System Test. Another is WiFiPerf. Either of these should be able to help you measure data throughput on your wireless network. I would recommend that you run a baseline with your current setup and rerun them after making any adjustments to see if you get an improvement.
Finally, is it at all possible to set up an entirely separate wireless network just for music streaming (and not for connectivity to the outside world)?