From a PhD applicant, they expect the following:
1. Focus and abilities--- This becomes evident in SOP and Transcripts and other things
2. Fit in the program--- Partly this becomes evident in SOP. If they ask for PHS in addition to SOP, IMO, they are looking for the following:
(I have worked with lot of students on their SOPs but not too many students on their PHS. So all this is just a suggestion from my side. See if it makes sense to you).
1. Your evolution into a student that makes you a suitable PhD student. PhD requires lot of commitment and focus. Your experiences that helped you develop these qualities will be highly valuable.
2. PhD also requires lot of self motivation. In your life, have you come across any specific instance because of which you are all the more motivated to pursue PhD in that field?Suppose you are in some situation that you desperately want to come out of, if you can show that higher studies (in your case PhD) will help you overcome that, that would be terrific.
Some suggestions:
1. You have mentioned the names of a few schools that you have been part of and your experiences there. See if you can relate that with how it made you a better person--how that made you a more self motivated and a focused individual.
2. You have mentioned that most of the income of your family came from your mother and such other things. But there is no logical conclusion to that. In what way those experiences made you a better person?
3. Consult others on whether you should mention your homosexuality in the PHS. It is your personal inclination. How is that related with being a good PhD student?
4. When you mention political angle of Russian Federation, it appears that you somehow are not happy with the way things are going and you are looking for a way out. Correct me if I am wrong. As mentioned in point 2 above, you need to be able to demonstrate that PhD is the right vehicle for you to come out of whatever situation you find yourself in.
As I said earlier, I don't have as much experience with PHS as I have with SOPs so treat all these as my suggestions and nothing more. Implement them only if these points make sense to you. Consult others if you wish to doubly confirm.