2) This is not true
The team who's behind will try to foul your worst FT shooter.
So yes, in the end of the game when this tactic starts, you will see that your best FT shooters won't go to the line that much anymore. So it's not a bug as well.
The moment my player got the rebound he got fouled. But the rebounder never went to the line, even though I would guess he's the one being fouled as it happened in the same second.