If I delete the files on the computer’s Dropbox folder does it delete them from Dropbox

There doesn't seem to be a way to do this at the time. Using Windows shortcuts is one possibility to make it as though the files are located in the same folders, however, it seems like it would get a bit complicated if there are a lot of folders.

There is a feature request for this exact issue, which you can vote on.

Other features you may want to look for is the ability to watch any folder, which you might be able to use in conjunction with your file system to create a limited set of folders to sync. Another one that might help is excluding certain file extensions, this would help if all the large files are of the same type (e.g. .exe, .avi, etc.).

It appears that the files were not mine to delete after all.

Right clicking on the folder brings up the context menu - the first option of which is Shared Folder Options. Clicking on that option shows the following dialog:

In this case I'm the only member on the list so it's safe to delete the folder. In the other folder there were more names on the list - the person who shared the folder in the first place and others. In this case it would NOT be safe to delete the folder as it would delete it for everyone else as well.

The correct action here is to click on the "Leave folder" option. You get the option to keep the files on your computer and then on OK your usage is reduced by the size of the files that were in the folder.