You got good deals on both machines. Congrats ! The Superdrive will certainly come in handy to make 800k floppies for the Plus later. Why?
Because the Plus doesn't use the same floppies as the SE Superdrive. So if the floppy you're trying to boot from is a 1.44meg (HD) floppy, the Plus certainly won't boot from it. You can tell DD floppies and HD floppies apart as HD floppies have two holes (well one hole and the write protect notch) and DD floppies only have the write protect notch.
If the floppy you're using is a 800k one and works with the SE, then you definitely have a problem with your floppy drive or bourns filter.
You should take it apart and clean the heads with Q-tips and isopropyl alcohol.
You don't need the batteries, in fact I'd say it's better to run these machines without any. You'll have to take the SE apart at some point in the NEAR future as some batteries referred to as the "Diabolical Red Maxells" tend to leak and kill the logic board. Maybe you got a Maxell in there... You can't tell until you take it apart.
I'd say this is your first priority here. Get a suitable (long) Torx T15 screwdriver and take this baby apart. There are 4 screws on the back (the Plus has 5). You need do disconnect the floppy drive, the HD and the logic board cables. Be careful not to snap the neck of the CRT while you pull these cables out. Be very gentle
You should be able to swing the logic board out and remove the battery. If it's not a red Maxell, remove it anyway. It's safer.
About the external HD20. There is an HD20 repair utility out there but perhaps the drive itself is fine and the system file is just corrupted (or maybe there's no system file on the disk?). Since the Superdrive works and is compatible with the HD20, you can go ahead and plug that HD20 into the Superdrive's floppy port. If the Superdrive can't boot from the HD20, it will boot from its internal drive. If the HD20 still doesn't show up on the desktop, then run the HD diagnostics available
here (you'll have to create an account there if you haven't done so yet.)
Hope this helps.