Hands not part of the bat

[Chess Ref]

Okay. I am a 1st year ump. Enjoying the heck out of it so far.
I understand hands are not part of the bat so I now have several questions around that.

1. Batter hit by pitch on the hands--Awarded 1st base- true

2. Batter swings at pitch-ball then hits hands-foul ball--true.

This is what i am thinking occurs in these two Sitch..

Feedback would be greatly appreciated.. Thanks