You can apply a cross-dissolve to the audio edit, so the audio transitions smoothly between clips. Click on the transition point on the timeline to select it, and then type Command + Shift + T. This should apply the transition.
You can control- click on the transition and adjust the duration of the transiton by choosing Duration from the drop down menu.
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.
back in the day (a long long time ago) with my first avid media composer, I would get a pop on almost every edit and need to apply a one frame dissolve. Can't remember the name of the sound card. Nowadays, I rarely if ever get one and when I finish a piece, I always listen very closely with headphones. I suspect it's just that the hardware/software has gotten better. If you're getting them all the time, I'd suspect there's a format problem. Shouldn't be happening constantly.