Mentioning LGBTQ Identity in Personal Statement for PhD Applications
Edit (in response to revised question): 

In light of the revised question, this sounds like exactly the sort of thing they are asking for, so yes feel free to talk about L, G, B, T, Q and X.  However, my guess is that whatever you write here won't make too much of a difference (as long as you don't make yourself sound crazy or anything), for the same reasons I indicated in my original answer.  

Original Answer Below (where it sounded like this was about a personal statement):

Unless they are asking specifically for you to address diversity issues, I don't think it matters much what you say about LGBTQ issues in your personal statement, as it has nothing to do with physics.  Note: depending on the department and admissions committee, the statement of purpose may be important or not important (e.g., Why do admissions committees consider the Statement of Purpose to be important? and How important is the statement of purpose in a PhD application for admission to a top school in the US?).

What I look for in a statement of purpose (in math, which I imagine is similar to physics) is basically what I look for in the rest of the application: your preparation for grad school, your talent and work ethic, your interests/fit with our program.  Though it also helps to get a sense of your personality (so it's not good, e.g., if you sound like a crackpot).  

I don't think the issues mentioned in your question reflect too much on these things.  On the other hand, I don't think it will hurt your application if you want to briefly mention at least (1) and possibly (2) if you can weave them in naturally, but these things shouldn't be the focus of your personal statement, as they say nothing about why you want to go to grad school.  (Certainly your CV is a suitable place for (1), so it can make it onto your application there.)  Academia is relatively LGBTQ friendly in my experience.  However, we don't want to know your whole life story on your application, just the part of your story related to (in your case) Physics.