1) An I-frame (or key frame) is one that does not depend on any other. A P-frame is one that involves prediction/compensation from other previous frames. A B-frame is one that that involves prediction/compensation from previous and future frames. B-frames are good because they are small. With a good encoder/format B-frames don't have to look bad.
2) Psy-rd is a psycho-visual adjustment in x264. It try to retain a similar frame complexity as in the original because this looks good.
3)
x264 supports psy-rd. What is it? You just asked and I just answered. For more see:
http://forum.doom9.org/showthread.php?t=138293
4) Yes but more makes x264 slower and there are level-related restrictions.
5)
x264's verbose switch is --verbose (-v for short). In future check x264 --longhelp
Finally: H.264 is a video format, x264 is an encoder for that format.