Export and embed are completely different, see here on how to embed.
But for full screen, there is a behavior with indie that lets you click an in-game object to full screen the game. BUT as well, there should be an option inside the itch page settings to enable a full-screen toggle at all times in the corner of the game.
Edit: I did some testing with one of my games where I used the itch full-screen option. It only puts the game into the top left corner, not sure if this is something Grazer can fix or something I need to look into to add with the imbed code.