If I had set up mail forwarding from my Barnard email account to another email account before migrating, will I have to set it up for my gBear account after I migrate?
Since the Barnard email account will stop receiving email as soon as they migration, nothing will be forwarded from that account after the migration. If you wish to continue forwarding Barnard email to another account, you will have to set up forwarding again using your gBear account. See Google Mail Support for instructions on how to do so. However, everything forwarded to your Barnard email account will show up in your gBear mail account.