1. Are the updates for MS Office that are critical security things included when you do Windows Update? (For example, there are a number of things listed here towards the bottom: http://isc.sans.org/...ml?storyid=2232 -- would those have been included in the last batch of critical Windows updates?
All of my computers do Microsoft Updates, so I can't check it. But I don't think they would have been included. To confirm/deny, go to Windows Update and click Review Your Update History. This will show you the updates you've installed. Look for these updates that were released last Friday (I'm listing only a few of the 15-19 updates for Windows and Microsoft Office): KB920813 (Security Update for Office 2003), KB929057 (Security Update for Word 2003), KB929064 (Security Update for Office 2003). It is important to install the Office security patches, because.... they're security patches.
2. Do you need the GDI+ thing to do Office Updates?
I really don't know if it's necessary with the new Microsoft update site or not. Try it without, and if it doesn't work, they install it.
3. When you go to the Office Updates site, it wants you to install and run some kind of Active X thing. Is this necessary? And can it cause any problems?
Yes, this is necessary for the new update site to function. And no, it doesn't cause any problems.
4. Can doing critical Office updates (separate from whatever, if anything, that comes with Windows Update) cause any problems or conflicts with other things on your computer?
Periodically, updates will cause conflicts with other software. It's fairly rare, but when it does happen, you can uninstall the update or call Microsoft's Security Patch Helpline at (866) 727-2338 for free support (does not apply to service pack problems).
I hope this answers your questions and concerns. I highly recommend you migrate to Microsoft Updates. It works the same way as Windows Updates, in that if you want, you can control when and which updates you download and install.