I don’t think Bae knows Rumple killed Milah. That would have been one of the first things he brought up when reunited with his father in Manhattan.
In fact, I don’t think Hook knew that the boy he meets was Milah’s son (not at first, anyway).
I think either one of two things happened:
1) Bae found out that Hook was out for revenge and wanted to kill his father and that’s why he fled Neverland without Hook ever knowing who he really was -or –
2) Hook eventually did find out that Bae was Milah’s son, tried to get info out of Bae about how to kill his father and that ‘s why Bae fled Neverland.
Either way, I don’t think Bae mentioned anything to Hook about how to kill his father.
Why would he? He didn’t want him dead.
They associated the fact that Hook knew there was a magical weapon that could kill The Dark One with knowing about Belle. I believe they did that for a reason.
I agree with TGK – whoever told Hook about Belle also told him about the ‘weapon’.