I don't think I am the right person to perfectly answer your questions but I am applying for public policy master program this year so maybe I can share some of my thoughts :
1. When I was finding the right programs to apply to I briefly looked into the ones you mentioned ( I am a freelance interpreter and have a master in Translation and Interpreting, zero experiences closely related to policy, so these programs are obviously beyound my reach). Most of them are targeting at mid-career professionals, people who are at management level in international companies or governments, so I think you are the perfect fit for it.These are really prestigious programs, and you have a good GPA (which doesnt really matter considering your experiences) and rich experiences in the exact field you want to apply for.I think the bigger question is if the program is useful for you.
2. I don't think age is ever a problem when it comes to academics. I read it somewhere on the school websites that the average age for these programs are 26, but I dont think they have a age limit for it. Since most of them require applicants to have 5 + years working experience, JHU even requires for 7 years working exepriences. Also, I have a friend who got his MBA from Standford when he was 35, so it is more important to look into their courseworks and choose the one that attracts you the most.
3. I don't know anything about the funding on Yale's M.A.S. However I think for Standford, you have to be a Standford student or an alumnus to apply for its master of public policy, or there is another phd program you can apply for (not very certain though).
From what I know, public policy/administration focus heavily on applicants' experiences, and from this perspective I think you are a strong candidate. Hope this helps.