I have a .cls file I created in one Org. I pulled it down from that Org, copied the .cls class from the "classes" folder of that project to the "classes" folder of another project.
When I right-click the "classes" folder in Solution Explorer, I choose ADD... then EXISTING ITEM...
First issue, the popup FileDialog has "SOQL, Anonymous Apex Files" as the file types to show. It should default to show class files with a ".cls" extension, since I am on the "classes" folder.
Second issue, I type "*.*" into the File Dialog to override the default file type(s) so I can see all the files in the folder. I highlight the file(s) I want to add, click OPEN, the window closes, and no files are added.
Third issue, The ADD... NEW ITEM... context menu will add existing files. If I try to add a new file, and I give a name of a file that already exists but is not part of the project, TWS adds the file name to the project, and it appears in the Solution Explorer. But when I open that new file, it contains the code from the existing file that was already in the folder.