<chuckling> That pic is just so boxer! LOL. Don't mean to laugh, but seeing her in the background, and the slop of her ears, I'd say she may have a little guilt going on.
As for the trash, I think it's perfectly normal for her to scavange what ever little scrap she can. She may have never had a full meal or a regular one where she came from, so she does what comes natural. Again, this will improve as her meals become more regular. See if you can find a way to strap the lid shut or purchase one that you can. All my rescues would get into the bin, and still do if I am not diligent in putting them up high. It may also benefit you if you can close the bin in a closet, cabinet, or even outside the door. Keeping it out of her sight is a good idea for a while.
I have no idea about your vetting system there, but Roge sure does and gives great advice.
Good luck with the vet! Tell them the story how she came to you and I bet their hearts will open up as big as yours!
LISA ~ Lily LaRue - 4/07 boxer; Buster McDoogle - adptd 6/07 Vizsla/Besenji mix; Annabella Kanicki - 5/08-7/09 staffy; Mr. Smiley - 4/10 Boxer/pibble mix; Fozzy Bear - 5/10 Red Heeler/pibble mix