I have a dataset that contains information on applications to any job vacancy in an organization. I want to know if my Y (Y=1 if the application is from a woman) depends on the nationality of the applicant, so I created a dummy for every nationality (there are 36 in my sample).
Here are my questions:
1) How can I interpret the relation between gender and nationality with all these dummies? Does it make sense to include all of them (or to include n-1) in the regression?
2) How do I interpret the coefficients in Probit?
3) How to calcolate the margins given all the dummies? Should I do it for all the variables?

Thanks a lot for any clarification you might have on this!

PS: My other independent variables are all categorical: whether the application is internal, type of job, year of the application (here I also created multiple dummies for 6 years), years of experience of the applicants.