Is a degree transferable? Example: Can someone with a nursing degree from China come to the U.S. and work?

If you want to come to the US to work as a nurse, you would have to pass the exams, CGFNS, NCLEX and the English proficiency test IELTS. These are the basic requirements, of course, some states may require more.
More than that, your school must already have graduates who were employed in the US. If you are the first graduate of your school to apply, you would have to provide them with all the documentation of your curriculum if it is compliant with the requirements for nursing.

The degree has to be recognized by the receiving country...

If the U.S. recognizes the Chinese degree, sure you can work here...chances are they don't....

International degrees don't transfer well, unless of course it's like, Harvard, Yale, Oxford, Cambridge, University of Toronto, etc

Some degrees are transferable, some are not.

Some degrees, like nursing, M.D. or dentistry need to be approved first, and then you may need to take some classes and tests to be able to practice in the US. Depending on the career, the process may take from a few months to several years.

No. They usually have to go through whatever state they end up in. There are very strict guidelines. Normally it takes time and more classes to get a license. Some may have to go through a whole course again. They also have to get a work visa.