Question: Is a dmg compressed?
(I assume it is. Otherwise, why would it be the method of choice for distributing software online.)
A .dmg
MAY or may not be compressed. It may also be encrypted if desired.
Question 2: What is a sparse disk image, and what is a sparse bundle disk image?
A
sparse disk image is a form of disk image file that can grow or shrink depending on the size of the files contained within the image.
A
sparse disk bundle is a directory containing a number of files or
bands, each a fixed size (8.4MB in OS X 10.8) that makes it possible for Time Machine to more efficiently manage its data.