There's no way to run a SPARC binary on an x86 machine unless you wrote an emulator for the SPARC CPU and ran it.
Yes, as long as they are in proper format, with DOS partitions, etc. (However, because they are more tempermental, please back up your voice profile more regularly)
I had many problems when I first started with the Iomega Zip on my GS and it isn't the most reliable thing - But it works. Attach a terminator adapter to the back of the remaining port on your external HD - The Zipdrive has a weak termination and requires another terminator source. Last, if you are working on the GS for a long time and suddenly the Zipdrive Icons don't pop up when you load Finder, simply eject the zipdisk and push it back into the drive.
I have had a Zip Drive hooked to a CMS SCSI card (1990 ROM) for 2-3 years in my IIgs without a hitch. Basically you just go into the setup for the CMS card. It will partition the drive into 32 meg sections which you can access two at a time-- It makes three on a Zip disk. Then once GS/OS is booted it tells you that the disk is unreadable and asks if you want it formatted and you hit ok for each virtual drive and there you have it.
This is theoretically possible, but would require a very extensive amount of work. Your best bet is to get a SCSI Zip drive, and connect that to an Apple II SCSI card (see section 4.15 above), and use that. Here's a rundown on the problems with a parallel Zip drive: such a connection requires a bidirectional (2-way communication) parallel card. 95+% of all Apple II parallel cards are unidirectional and won't work, except for the rather rare Apple Profile controller card.