Scroll over your emblem, click edit. On the left, you'll see the layers, and the different colors. Click the bottom one, the thickest one. That's the background, you can change the color, or you can click the white box with the red line through it, that removes it.
Dude yes you can. It could have been a glitch, since it was when the character wheel wasn't working and I was stuck as Michael. But I was jumping into walls and down stairs and it was f'cking hilarious. You can punch, but you can't bring up the weapon wheel and you can't attack your family.