I might be able to chime in on your second question. I applied to Texas schools as an OOS student, and I decided that I would talk about being gay and growing up Mormon on my TMDSAS primary application. I debated about whether that was smart or not, but decided to go ahead a do it because A) it made sense for based on the essay prompt and B) I realized that I really didn't want to go to a school that would reject me if they knew I was gay. I had spent too much time in the closet and was not planning on stepping back in for med school. I applied to about half of the schools in Texas, and I ended up with interviews at UTMB and UTHSCSA, which was about what I expected going in with my stats and OOS status. During my interview at UTMB, one interviewer spent a lot of time talking to me about LGBT life at the school and assured me that I could be happy there, which I appreciated, and I was accepted at (and will be attending) San Antonio.
Ultimately, I don't think being out on the application really helped or hurt me at any of the schools where I applied, Texas included. That being said, I'm glad that I was, if only because I know that the school I'll be attending knows that I'm gay and they still want me there. I don't know if that is a common concern for other people, but it was important to me, mostly because of what it was like for me growing up as a scared gay kid in small town Utah.
TLDR; I was out on my primary TMDSAS application, and I got accepted to a school that I was happy with.