Actually, it's not that bad, which, perhaps is unfortunate, since I have a major production project that exists in about 5 different versions on my system right now. It's a sordid tale involving a programmer who made an unauthorized commit to the main trunk and a Beta Tester who doesn't have enough time to finish testing. All while I'm trying to do development AND support temporary fixes to the current production source.
If you want 2 copies of the same project in the same workspace, just check out another copy, but override the project's folder location on the checkout dialog.
If you literally want to replace what's in a project with an alternative version of the project, you can either brute-force delete the current project using the Project menu/Delete + Delete Files option followed by a new checkout OR you can do a Team/Switch Branch/Tag menu operation.
Per-project settings are (mostly) contained in the ".project" file that's in the root of the project. Classpath settings are in the ".classpath" file, but with careful design, the classpath can be made portable. Both of these files are straightforward text files and may be manually edited, but for best results I recommend only doing so when Eclipse is not running (or the project is closed).
"privilege" comes from the Latin words for "private" and "law" (legal) and dates to feudal times. To "claim privilege" meant that you were above the laws that applied to the common people.