1. I don't think it matters when you introduce the server. Though I would wait until after you upgrade so you don't have to upgrade two media servers.
2. In the Media server properties remove the current media server and add the second. Redo your policies to point to the new media if required (.i.e. policies aren't set to Any Available.
3. Without built in code running on the SAN, I don't believe any software can start a Fibre stream from one SAN to another. We use IBM DS products here and they require a separate license/firmware to do SAN snapshots (as they are called in the IBM world). In other words, yes, your data is traveling up and down the same HBA. Shouldn't really matter much though as Fibre is full duplex and your limiting factor will be the write on the destination SAN, not the HBA.
4. Not if it the backup SAN is purely used for backups. The only that would need access is the new media server. If you do decide later that you need the Exchange server to see both SANs, you will need to introduce a Fibre switch and implement zoning. This is assuming you are using Loops only at the moment. If you already have a SAN fabric with Fibre switches, then all you need to do is configure the Fibre Fabric with a zone between the backup SAN and the Exchange server, then on the backup SAN allow the Exchange server as a valid host. Restart the Exchange server, or use Diskpart to search for and add the new LUN(s).
One word of caution: Our experience during the 5.x to 6.x upgrade was not very smooth. We ended having to recreate all of our policies, so make some good notes about your policies before you start...
HTH