I'm SFS 2012 but I will do my best to answer what I can
Since the the four schools are not separated physically, housing, environment and lifestyles are very similar. Everyone rooms together, eats together, and for some intro classes studies together. Each school has it's stereotype, but what I can tell they are just that- generalizations. The biggest difference between the schools is the curriculum. Each college has different requirements for graduation. For example, SFS requires a proficiency exam in a modern foreign language, four semesters of econ, passage of a class called map of the modern world, and a few other unique requirements, but no math or science. So if you want to study IR, apply to SFS, because the major isn't offered in the college. Actually it isn't technically offered in SFS either, unlike most schools where the major is just IR, at Georgetown you get to pick something more specific like International Politics, International History, Culture and Politics, International Science and Technology, International Law or International Economics and then certificates (like minors) into regions or focuses. That was a big draw for me. Because Georgetown devotes an entire college to IR, it has the ability to offer more than it's peer schools and attract incredible facility in specialized fields.
People like to argue about weather it's better to apply to the college because it's "easier" and then transfer in later. Personally, I think it's silly. To answer your last couple of questions, yes you have to apply directly to a school. One of your essays will be school specific (sfs asks you to write on a current global issue, the college is a "why georgetown"). SFS is self selecting. You don't apply unless you are really interested in IR, so it is harder to stand out. They are also looking for different things. Are you strong in languages? Are you well aware of world issues? What have you done to show that you are really passionate about IR? If your resume and essays and recs answer those kinds of questions then the adcoms will know that that is where you belong and won't understand why you are applying to the college. So statistically it is just a little bit harder to get into SFS, but I think (I'm not georgetown
) more importantly they know what they are looking for and it's different than someone applying to the the college. Plus I really enjoyed writing my world issue essay. It was a chance to show the school who I was as student and not another attempt to fit my personality into 500 words or less (though they did ask for that too).
Good luck!