#1. How is the volume being increased? Does the ATV have an internal amp?
It won't have a power amp if that is what you are meaning. If your connection is digital; the digital signal will be sent through through the DAC in your receiver then to a pre-amp in your receiver and on to the power amp and to your speakers. Information about the volume is carried by the digital signal to the receiver which is responsible for adjustment to the analogue output needed for the speakers.
If your connection is analogue; the DAC and pre amp in the Apple tv generate an analogue line level output which ordinarily would be fixed (subject to variation from the audio itself) so that the only volume adjustment you could make would be on the receiver. When you adjust the volume via the Apple tv, what you are in fact doing is adjusting the line level out to the amplifier.
#2. How can I be assured I'm no losing audio quality if the ATV is increasing the volume?
The volume adjustment on the Apple tv allows you to adjust the line level between zero and it's normal level (no volume control), if it were able to increase this level above normal level then yes you would possibly hear distortion, but the Apple tv doesn't do this.