Logshipping is basically doing backup and restore, so the same backup and restore rules apply, you can do it to the same version or a higher version.

But once you have restored to a higher version and made it active, you cannot logship back as you will be going from higer version to lower version which cannot be done.

So best in a logshipping environment to have the same edition and level of SQL on both source and destination.

Logshipping and backup restore doesn't care if the server is 32 bit or 64 bit.

SQL 2008 to SQL 2008, logshipping will work ok, can fail back

SQL 2008 R2 to SQL 2008 R2, logshipping will work ok, can fail back

SQL 2008 to SQL 2008 R2, logshipping will work ok, CANNOT fail back

SQL 2008 R2 to SQL 2008, logshipping will NOT work,