3 frame audio dissolves and 48K audio will lessen these problems a great deal.
Dramatic sound changes can also be caused by the levels of the clips being different.
There will be many opinions on the best way to mix but ensuring that clips A & B are at similar levels will also help with this. I would suggest looking at the meters to get a better sense of how loud or soft something is. I find this far more effective for adjusting the levels of a clip than just doing it by ear.
The pops are most likely being cause by where the waveform is being cut. When you zoom in(very far) and look at the waveform you will see where the waveform is above and below the zero point. Whenever possible make your cut in the waveform at the zero point(or as close as you can get it) vs. above or below. This may mean adjusting your in or out point by a frame or two but it will clear up 99% of your problems.