(1) You don't need a humongous amount of disk space for the operating system: I installed enough of Leopard on a 16GB USB flashdrive to be able to get my system up (IIRC, I didn't install all the available fonts and languages). But it was incredibly slow: perhaps some of the problem is the USB, and firewire might do better
(2) Required memory probably depends on what you intend to do once you boot from the partition. If you're planning to use this as an emergency way to continue working if your internal disk dies, you need room for whatever critical programs you have on your internal drive. Most apps will produce a fair number of temporary files as well, and some of these will be stored to disk, so you'll need some space for that
(3a) If you plan to use the boot-up partition for recovering some TM data in the event of an internal drive failure, then you need to allocate some space for that also. But my guess would be that's not a particularly good idea -- it may not work well: you'd be asking a single head both to read from one partition and write to another, and I'd expect that to be very slow if there's a lot of data to copy
(3b)For my own machine, I decided to set aside one disk for TM and another as a bootable recent clone of my primary disk -- then, if I have to rewrite or replace my primary disk, I've got a fairly recent copy from which I can approximately restore, after which I'd hope to use TM to complete the restoration
(3c)If I were going to try doing what I think you want to do, I think I'd want an external drive of size at least ((size of my primary drive) + 1.5*(maximize size I expect to use on my primary drive in the next few years)), and I would set one partition to be the (physical) size of my primary drive and give the rest to a partition for TM: then I would clone my primary drive to the first partition, after which I would set up TM to use the drive
(3d) Here's another idea, but I don't know whether it's good or not: partition your external drive so that one piece has enough room for your original install disk:
http://www.macosxhints.com/article.php?story=20071025021604930