I am a new user to both Newsgator with Outlook 2003 and the Online synchronization with web based edition. I have a lot of feeds so I want to create folders for each topic. I am creating a hierarchy of folders with topics. For instance I have a "Apple" folder and I assign multiple feeds to this folder and then group them by "feed Name" in outlook 2003. This works well, but they don't show up in the "web edition" when I use these folders.

Does the web edition only work with feeds in the root of my "My News" folder? 

Those feeds should still show up in web edition; you can switch between feed and folder views in web edition, and you should see that you have multiple feeds worth of content in certain folders, if you've mapped multiple feeds to that folder.

If there is a "placeholder" folder in Outlook which is only there to preserve hierarchy, where no feeds are mapped to it, then that folder won't show up in web edition.

Web edition does not preserve folder hierarchy from Outlook. We're working on this, and most of the code is in place to make this happen, but it didn't make it in time for the release.