If you want to be treated like a five year old I'd suggest...

If you want to be treated like a five year old I'd suggest reading "The Very Hungry Caterpillar"

Jokes aside, here is my answer to your very good questions:

"This sudden sell off by one institutional investor doesn't affect the dividends at all, correct?"
- Incorrect. Management has control over how much of profits are shared as dividends or re invested in the company or a share buy back etc.

"Whatever the SP is, is irrelevant to the slice of profit that is returned to the shareholders, is that true?"
- No. Management decides how much if any profits are paid to share owners as dividends.

"Or can FMG decide that the SP has dropped, so they will drop the slice of pie they are sending back to shareholders."
- Yes they can drop the lice of the pie they send back to shareholders.

"But that doesn't make sense to me, or am I missing something?"
- It depends on their strategy. As you have alluded to they can maintain the dividend to make buying shares more attractive and therefore boost the share price. Or they can reduce it and re-invest in the company for future growth.

"Moving forward, the SP in theory should bounce, because we're suddenly getting a bigger return as a percent of the SP, and the SP is largely driven by how big the dividend is."
- The most common reason for a share price drop is an anticipated reduction in profit. And when profits reduce typically the dividend does too. That's WHY people are selling (they think profits and therefore dividends will reduce)

"But, unless these sell offs are because they have predicted future earning drops"
- Yes that's exactly what's happening. The price of iron ore is going down so many people believe profits will too.

"for the LTH, it's just a matter of holding, or even buying in these lows, correct???"
- Correct. But then one has to ask how long do we have to hold for. if it's just a few months then yes, I'd say hold. But what if it's a few years?? Then it's possibly better to sell now and put that money into something else that will grow more quickly.