So, if I have understood everything correctly:
-Are you going to send me a picture of yourself? (with your face in it.)
-I'm going to send you a picture of you...I took it three months ago at your cousin's party, and you look really handsome.
-I like that picture of yours...I'm talking about the one you took of that humongous house with the trees in the background (a picture that belongs to or was taken by the person I'm talking to, but he or she does not appear in the aforementioned picture.)
-He sent me a picture of me. (with my face in it.)
-I'd like to send you a picture of myself. (again, with my face in it.)
And what about : "let me send you a picture of you"/" Please, allow me to send you a picture of you" are those sentences correct? Or, as I suspect, the correct way to say it would be: "let me send you a picture of yourself"/"allow me to send you a picture of yourself".
If I'm asking "you" to let me, or allow me to do something, the subject would be "you", therefore I need to use "yourself".
Does that make any sense?