Actually, the ".svn" folder does not contain settings, it contains Subversion context, and there should be an .svn directory for each and every project directory that is under Subversion archiving.
The Eclipse .project and .classpath files may be safely archived in svn, and usually should. Although for best results, they should not contain absolute file paths. You can avoid this by defining symbolic pathnames. I do that so that Eclipse can find my
Tomcat libraries, for example.
In theory, if you already have the .svn context is a project, Eclipse can be instructed to adopt that context, and yes, Team/Share is probably what would do it. Although for maximum safety, I'd get the Subversion administrator to make a backup of the Subversion archive and do this at a time when a botched attempt could be rolled back.
If that isn't possible, consider checking out a fresh copy of the project and manually merging in whatever changes you have made in your current project.
Also note that in SVN, the archive is presented as though it was a filesystem tree. This means that a "project" doesn't have to be one of the root directories of the archive, it can be any subdirectory. I checked one out just yesterday using a URL in the form of "https://subversion.mydomain.com/projects/projectxyz/branches/timh/branch1".