use quicktime player for all your needs
first open the file you want to convert (avi or mpg) then export it as a .mov one
or you can use avs video convertor for wide file format support.
for your second question i think you are playing with the output file quality settings, thats the only reason for such huge file size.
few months back digit has a trailer of half life hardly 20 sec video of 115MB+ size