Carl did murder somebody just because he was a member of a group that might be a threat to their group later, didn't he? Seems a decent reason to be afraid of him. But I actually didn't get that vibe in this case. He threatened to tell his Dad, Hershel basically said "Okay," and, realizing he was going to do it anyway, he came along. The situation was one where neither of them could really stop the other from doing what they were going to do (without stupid violence), so they went along with it.
As for killing zombies... there's always the threat at least with a gun, of drawing more... Carl had a makeshift silencer, but if he needed two shots, it's a risk of a loud bang, and, fundamentally, bullets are probably more valuable than taking out two more zombies (out of thousands in the area) that were basically crippled in one way or the other. Hand-to-hand is always a risk, especially with a one-legged man and a child. Just walking away was probably the right call.
The initial review mentioned that the leap to Carol came out of nowhere (I saw it coming, myself, due to her rather harsh criticism of the child for being 'weak' because she couldn't destroy her father's brain right after he died), but there's one piece of evidence he missed, Rick examining the hand-print, from which he could presumably gauge the size of a hand and know that it was at least probably a female. From that, her behavior, and her general pro-active nature lately (Carl already told him he was teaching kids to use knives), it's probably still a leap, but not as much of one, and it's not like he accused her in front of everyone, he asked to see what she'd say.