FED "almost" answers these questions on 2002 Interps 6 and 7. IN general, a batted ball that hits an object inside the fence "remains in play" and (by rule -- often ignored, I agree) cannot be a home run just because it "hits above a yellow line".
Scoreboard: If the ball continues across the fence without hitting a fielder, then I'd have a home run. If it stays inside the fence, then it's in play. IOW, I'd define the scoreboard as being the "fence" for that portion of the field.
Foul Pole: By tradition, a ball hitting the top part of the pole is OOP. I'd define the "fence" to include the lower part of the pole -- anything hitting the upper part would be a HR.
Tree: Keep the ball in play. Cannot be caught for an out. HR if goes over the fence.
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