I have never been able to successfully add a Form from an existing file to a new project.
I read on a blog that you add just the *.cs file and the depen
If you want to create a library of windows forms it is better if you create a Windows Forms Application project. Then delete the default form (Form1), go to the project properties and change the Output Type (or project type) from Windows Forms Application to Class Library.
This way the output will be a DLL but it will have the references you need for a windows forms project. As you pointed out, when adding existing items do NOT add their corresponding .Designer and .resx files, just add their top level/main file.