I'm by no means an expert but my comments maybe helpful to you.
Amplifier 1 - is actually nice integrated amp. This is first amp not based on Treshold (pass) tech. Its considered a nice mid tier unit.
As for pa7ii - your relatives almost got it right, as original pa7 amp is apparently a legend, but series II is where supposedly Nak started to seriously cut corners and as result Treshold sued them for keep using "Statis" trademark, while in reality don't really implement the design.
Control amp is another word for pre-amp (should be used together with amp like pa7)
Try to connect in this order :
Cd player -> control amp -> PA7-II amp -> b&w speakers.
p.s: Nelson Pass, CEO of Pass Labs - top end amplifiers, used to work for Treshold and Adcom before opening his own company
p.s: This forum is not big fan of most of Bose speakers and with good reason - they suck, especially tiny ones