I'm not sure I completely got your explanation of the dividend effect on stock price. A company's cash in hand is not a part of its stock price. It contributes to sentiment on the stock, but is not part of the stock price itself. I could be wrong. The dividend payout does not come from stock price, it comes from revenue and profit, no? And isn't a dividend a testimony to profitability of company?
Yes to all of your questions. But the point is on day zero (technically the last "cum dividend" day) you get the stock plus the right to receive a dividend the next day, and on day zero + one (the first "ex dividend" day) you don't get the right to the dividend, but everyone who was a holder yesterday gets the dividend. So the stock price drops by the amount of the dividend.
