What version of Rockbox are you using? The "Photo", "Colour", and "Video" iPods are all available in a 60GB capacity, which do you have? Please make sure to specify these things in the future.
This all sounds like you have not encoded your videos properly. Read the "How To Encode Files" section of that wiki page.
MpegPlayer can not scale videos for you, so if your video is bigger than the iPod's screen, some of it will be cropped.
Sound going out of sync is probably due to too large a frame rate and/or width/height for your player to handle. The "Performance" table on the wiki page should tell you what to aim for.
For regular playback, you should always have "Skip Frames" and "Limit FPS" options set "on". They are "on" by default, but maybe you accidentally changed them.
Converting to MOV will not help. You wouldn't even be able to play the video then. Rockbox only plays MPEG1 and MPEG2 video with MP1, MP2 or MP3 audio.