So if the beekeeper turns the brood box around 90 or 180 degrees all the bees would not be able to find the nectar source,
or at least until another bee comes back a with a new dance.
Yes, they would, because, as "caticind" said, the dance communicates direction and distance. So if the direction is "East" and the distance is "1000 yards", the direction of the hive opening is irrelevant.
The videos are great for us humans and we can see what seems to be happening as a whole but I feel the bees cannot see it as we do.
Exactly right - the bees don't see the dance, they feel it.