There is blood on Samantha's gloved hand when she presses the keypad, but there is no blood on the keypad after she removes her hand.
The B.F.G. is a weapon that dates back to the game "Doom" back in 1993. There, it was the 'ultimate' weapon which, when fired, cleared the screen of foes in a great sickly green blast, consuming enormous amounts of ammo. It has showed up in various later games by both ID Software and third parties. Up to this movie, the acronym was never explained directly - although Sarge's version, "Big f**king gun" was for a long time the community's accepted name (also used in the original Doom design document, but not the game itself), and is most likely a homage to that.