Comparing files

[Theo van der Merwe <ntvdm@xxxxxxxxxxx>]

I am still a newcomer to Linux and have the following questions: 

1) How do I compare the contents of files (binary), i.e. determine the
differences (if any)?
2) How do I compare the contents of a partition and an image file created
with the dd command (binary)?
3) Is it possible to apply 1) and 2) recursively over a complete subdirectory?

Thanks in advance for your help.
Best regards,
Theo (ntvdm@xxxxxxxxxxx)