If you wanna go into the numbers to understand how GXE works, you can check this:
https://www.smogon.com/forums/threa...layers-overall-rating-than-shoddys-cre.51169/
Now, from an empirical point of vu, you can note that your GXE will increase after winning a game and decrease after losing one, but the increase or decrease depends on the opponent GXE. Thus, the higher your opponent GXE is, the more your GXE will increase after a win and the less it will decrease after a loss. It also depends on the number of games you have played. If you already did a huge number of games, your GXE will increase or decrease very slowly while when you start playin g on an account its variations are relatively important after each game.
In my opinion, there's no point in trying to calculate how to increase your GXE as you don't choose the opponents you will face and the only way to increase it is winning your ladder games.
If you are talking about your Smogon profile picture, you need to click on your name in the top right corner of the screen, then go into the "Account details" section and you can change it here:
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