Yes, I would think it works better for black . . . what on earth is that knight doing there? Do you need a response for the wierd knight move? Or are you trying to justify it?
But yes, everything under 1.c4 is the English (although obviously transpositions can occur, especially to some QG lines). This doesn't look like any transposition . . . it doesn't look very good either. You can go to chesstempo.com, click on chess database-->chess openings--> and click on any random opening. It will pop up with a that opening, but you can hit the back button. If you hit "back" to a blank board, you can make your own moves, and it will show up most common opponent responses. I saw 0 times Na3 being played.
I started playing this opening today and I am curious to what it is called. I enjoy using it and I would like to put some research into it.
This opening does change depending on the opponents attack on the pieces. I noticed in my games that it seems to work better when playing black than when playing white. I posted a general idea of the opening. Black's opening was just a basic opening in this example. Others suggested it is a variation of the english opening but I want to check if there is any knowledge about it.