Well,
1. The .22's normally have a better BC, but its often easier to get higher quality pellets in .177. If you are shooting at 25yards/meters at higher power, say 20fpe and under, I think they are a tossup, as I see good work done with either, but stay away from .22 models if low powered (under 15fpe) and stay away from .177 if high powered (well over 20fpe). I think a longer ranges, the .22 is usually better.
2. Yes, the barrels are usually well rifled, though there is one company that only rifles the last inch or so (yet it still works ok).
3. Do the hand-powered air pumps really work? Yes, but they tend to be strenuous to operate and don't hold up well. Its REALLY difficult to service them properly and maybe just as difficult to GET them serviced properly. Also, they tend to allow moisture to get in your gun if the weather is humid.
4. Does the compressed air generate moisture? Compression of air DOES tend to create issues with moisture ... since it heats the air, and hot air hold more moisture than cool air. Once the compressed air cools, some of the moisture "falls out" of suspension. Good compressors, such as used in dive shops have a series of water traps to deal with the issue, but most I haven't seen air from small units and handpumps to be as "dry" in comparison.