– You should be able to use the same project, but creating a fresh one and copying across the bins is a somewhat safer way
– You should not have any issues with footage not linking; you could delete the msm.pmr and msm.db files from the mediafiles folders if only to force the Avid to rebuild these databases. It’s safe, but not required.
– Mac-PC should not matter at all, just beware that you should not use HFS+ formatted drives as media drives on a PC, nor should you use NTFS formatted drives as media drives on a Mac. You’re better off copying the media to a properly formatted drive.