This suggests that new distros can share the swap file, and maybe the /home partition too? Is that correct or have I misunderstood?
Yes you have understood correctly.
Like I said you get different oppions on partition sizes and formats, I stay way clear of ntfs, those other boys tell you to stay clear of fat32. So it's got to be your call. I have my reasons, some of which is based on my experience, the rest based on my needs. I also like a little more than 8gb for root. But that's me.
As for different distros using the same swap, and home. I currently have six unrelated distros running that way. There is only a couple of things you should understand about it.
If it's a laptop, and you use hibernate, you must reboot into that os next time, or it could cause file corruption. That's using swap on multiple distros. At least thats my experience, there might be a work around for that.
As for /home each distro must have it's unique user. Such as steve, mcsteve, and stevemc. So that they don't sqaush each others config files. With six distros installed, I have six users in my /home.
One last note, each distro install will require you to format the root and swap at time of installation, that's fine, just don't change the format of said root, form lets say ext3 to some other, or it won't mount in the other distros without fixing it. But don't format /home again after the first install, or you'll lose your home on all the other installs.