Yep.

For the sake of the math, I'll use a 5:1 split.

Day 0: Company trading for $1/share with 100 outstanding shares -- Market cap = $100. They are offering $0.05/share dividends -- Total dividend = $5

Day 1: Stock split at 5:1

Day 2: Company trading for $0.20/share with 500 outstanding shares -- Market cap = $100. They are offering $0.01/share dividends -- Total dividend = $5

Yes. Basically, a stock split changes nothing about the value of the stock. However, it might lead to a slight rise in the stock price since small investors will now find it easier to buy, and so total demand for the stock might be a bit higher.

Yes, but math/wording not quite right. It will decrease by 6/7 (or be 1/7 of what it was).

Yes. Dividends are % based.

This article has a little more information, stating that this quarter's dividend will be exactly $3.29 per share of common stock for all shareholders as of 5/12/2014.

http://www.streetinsider.com/Dividend+Hike/Apple,+Inc.+(AAPL...