First post -- multiple questions

You may get some better answers, but I'll try to get the ball rolling, as you're trying to do something almost identical to what I have set up at home.

Generally, no--this should work quite smoothly. You can also make a clone of the old boot drive to an external and use Migration Assistant on that, if you want to avoid the FW800/400 adapter.

There are a lot of ways to approach this. MobileMe probably is the smoothest and easiest if you're syncing preferences, but it of course isn't free. You can do a roll-your-own MobileMe, but that can get pretty hairy.

An alternate, if you want to get fancy, would be to buy one of the new(er) Mac Mini servers, which will let you create network home folders on the server; you then log into that account in effect, and get exactly the environment you want whichever computer you're sitting in front of. (This feature isn't available on client versions of the OS, and OSX Server costs about as much as the mini with the software if you buy it alone.) This has the added advantage of being able to store all your data on the server and access it via the network, so it's wherever you are (so long as "wherever" is at home). It's also possible to essentially sync against the network home folder to a laptop so that you have access when you're not at home without issue.

I do this, except without the network home folders, because the mini Server wasn't available at the time--I just have all files directly on the server, and use IMAP for mail.

Apple will, hopefully, come up with a more user-transparent way to do exactly this in the future, as a lot of us want to without the hassle. MobileMe currently is what's filling that niche.

For most applications, yes, but due to the fact that the network is MUCH slower than the hard drive, I wouldn't recommend it--you're unnecessarily slowing down program launch and anything that requires it to load stuff by a LOT, and your only gain is a few dozen MB of space.

I'm backing up directly to my Mini server instead of a TC, but this should work just fine, even with multiple computers, so long as there's enough space. Be warned, however, that there has been a lot of reports of glitches with Time Machine backing up over the network--it has a tendency to corrupt the backup disk image (which won't happen for direct access). In my testing an external hard drive connected to an AEBS (not a dedicated TC) was unusable--it would repeatably corrupt the backup image after a few tries, apparently because it just couldn't handle the data throughput. Backing up to my server over the network has been reliable for the last year, although I admit I only do wireless backups once in a while--most are via a wired gigabit connection.

So long as you're SuperDuper-ing to a physically attached drive, though, you should be safe regardless.

Maybe. If you plan on accessing your home computer from somewhere outside your home network, you will need to forward the correct port(s) for the service you want to use, so that connection attempts from outside your home network get routed to the correct computer. Further, unless your ISP gives you a static IP address (few do, although they don't usually change often), you'll need to use a dynamic DNS service (there are many free ones), coupled with an application on your home computer that updates the service so the dynamic DNS service knows where to route your connection to. As a result, you're probably going to need to leave your iMac awake for this to function if you're going to be away from home for more than a day or so, otherwise the IP address might change and you'll no longer be able to find your home network from a remote location.

All that said, if you do have it set up to forward the port(s) and you have the IP address of your home internet connection, you can wake the iMac remotely if you have Wake On LAN enabled. Apple has a simple system for doing this automatically set up, but it will only work if you're within the Airport network, not from the outside, and in my experience it "Forgets" sleeping computers after about half a day. So you'll need to download a remote wake app (WakeOnLan is a simple free one) to poke your home computer. You'll also need to forward the wake port at the router, and set up the iMac to have a static IP address so that the forwarding will work.

If this sounds a little complicated, that's because it is, and there isn't really much way around it. I believe (though have never tested) that MobileMe has some features to try and simplify the process considerably--maybe someone else can chime in to confirm or deny.