I applied to Georgetown but also no response yet and not sure when they send out emails.
For writing samples, I have a family member who has been on a lot of academic committees to distribute scholarships and stuff like that, so not the same as a PhD but I assume kind of similar in spirit. He basically told me that a committee looks at writing samples like you probably imagine, ie. they'll look at the abstract, first few pages, conclusion etc., but no one has time to read 20-30 pages to check if you have some spelling mistakes or typos in the body of the paper.