Everyone recognizes that's a joke because obviously the number and shape of the pieces doesn't affect the size of the pizza. And similarly, the stocks, bonds, warrants, etc., issued don't affect the aggregate value of the firm. ↗
Of course. I favor passive investing for most investors, because markets are amazingly successful devices for incorporating information into stock prices. ↗
If each of your time steps is one week long, you are not modeling the stock price terribly well over a one-week time period, because you are saying that there are only two possible outcomes. ↗