Outlines aren't an absolute requirement—they're intended to provide a value contrast with the environment. If your sprite is distinct enough from the background he's being placed on, you don't need one. Your little guy should stand out more than enough against green, grey, or brown, all of which are common background colour selections.
The second animation looks a bit odd because the arms and torso are so static. I realize he's carrying something in both hands, but there should still be some movement of the arms relative to the torso. And to be honest, the position he's carrying the whatzit in looks like it would be uncomfortable to maintain for longer than it takes to lead up to a pole vault.