As an undergraduate student, should I put my temporary address and manuscript on my CV?
For an undergrad, it is fine to list papers that are not yet submitted.  List them as "in preparation".  Also, if the REU requires letters of recommendation, ask your letter writers to comment on the status and quality of the project.

Yes, the address is just in case someone needs to send you physical mail.  Any place where mail will reach you is fine.  These days I'd say you could just leave it off, since it's unlikely anyone would actually need to do that.  If the program is limited based on place of residency, there would be a specific question on the application for that.