1. 6-1-3... For the set position ... "Before starting delivery, he shall stand with his entire non-pivot foot in front of a line extending through the front edge of the pitcher's plate..." Penalty - Illegal pitch... w/ no runners on, ball to batter... w/ runners on illegal act is a balk. If as you note "and the back of the right foot heel is in contact with the rubber.", then as a base guy (won't see that from the plate most likely) I'm probably going to say something to the pitcher in a way such that no one knows what we're discussing. It's the don't pick the scab. I may "employ" the first baseman to help me ;-). From "A" it'll be awfully difficult to tell if his right heel is actually touching the rubber because I have the left toe pointing at me. From "B" - I'll see it and say something quietly. Although part of me sees absolutely no advantage to that position. In fact, it's got to be damn awkward to stand that way on top of a hill.
2. I agree with others - I got nothing. I will assume he came to the set position. That is he started in some other manner, brought his hands together and was bringing them to their "compete and discernible stop" position. If he started with his hands together, then came to "another stop" - that's a balk (I've seen that too). The one thing that wasn't clear from your description was "raises his right leg (hang move)," - if you mean he pauses his leg for more than perhaps a half second in the air, then I've got a balk for stopping (no continuous motion after set). Another thing that is a balk is if after coming to the set position you take your hand off the ball unless of course you step completely backwards with your pivot foot behind the rubber (think swatting a bee or wiping the brow) - that could be what that BU was thinking about - easy to misinterpret. I can only hope his partner and he talked about it after the game. With regard to the step and throw - for a lefty especially it's important to make sure he steps ahead of the throw or as it gets drilled into your mind makes progress towards the base. For the lefty that does that simultaneous step backwards and throw to first without moving the free foot - just know what happened first. If the hands moved prior to, then balk.
As for who watches what - it's a pregame discussion with your partner, but for a lefty if the PU watches the legs and the BU primarily watches the hands, then between the two picking up any illegal stuff by a left should be achievable (especially whether he's going home first - IOW that magical 45 degree line).