> The desire now is to have a copy job, which will copy a filesystem
> from a Red Hat Enterprise Linux 5 server, over to a windows fileshare.

   Why?  What's in this "a filesystem"?  Do you plan to use the data on
a Windows system?  (Does "a filesystem" include text files which will
have the wrong line endings for many Windows programs?)  As before,
knowing what you're trying to do would make offering useful advice
easier than knowing how you think that it should be done.

> 1) Is CIFS the correct filesystem to use?

   Does it do what you want done?

> 2) Should checksum's be the same between the two filesystems?

   If the data are the same, then the checksums should be the same. 
Your 'surplu's of apostrophe's 'seem's to be bigger than I thought.
Try a Web search for these keywords:
      eats shoots leaves
Throw in "apostrophe" to narrow it more.