It doesn't seem likely. The internal interface is SATA, and I doubt there's any way to adapt it.

There's no problem that I know of, except to exercise care not to mistreat the drive while moving it around.
You might find a 2.5" portable more convenient.

Your ports are shown in the manual as SATA 1 Primary, Secondary) and the same for SATA 2(P,S).
Again, the manual isn't clear, but I'd assume these ports are adjacent.
I should also mention that you...

The manual just isn't clear about this.
Try connecting both HDs to:
The same channel.
Different channels.
How are they connected now?
It's possible you need a BIOS update.

Look in the BIOS under "Integrated Peripherals" and make sure the SATA secondaries are enabled.

Is there a RAID setup involved? What's the BIOS setting for these ports?
My board has 4 SATA ports, but doesn't support SATA Optical drives.
I can't tell from your manual whether yours does or not.

Motherboard model number?

I think the only issue here is the swap file.
Windows needs approximately 15% free space to function efficiently.
This issue confuses many people, but as far as I can tell, you are...

If the drive is installed properly, you need to format it.
Right-click My Computer/Manage/Disk Management
Look or a drive that's unpartitioned, probably below the C drive. Right-click to Format NTFS