Self-employed working for overseas Non-Profit

I am retired but do consulting for an international non-profit based in Belgium.  I have no other clients.  I invoice them quarterly for the work done, which also includes serving as editor of their quarterly magazine.  I am paid via wire transfers to my US bank from a European bank.  I occasionally travel overseas for various projects, including meetings in Europe and at headquarters, but most of my work is done from home.  I receive no 1099 nor other forms since they are not a US organization.  So: 1. Am I considered self-employed in the full sense (able to count expenses against income) or as an employee who uses Schedule C because it is the only option for reporting income in such circumstances?  See the IRS page "How to Report Wage Income Paid by Foreign Governments or International Organizations"?   2: Do I pay Social Security/Medicare Taxes?