Why do we use the overall cost of capital for investment decisions even when only one source of capital will be used (e.g., debt)?

In computing the cost of capital, do we use the historical costs of existing debt and equity or the current costs as determined in the market? Why?

Why is the cost of retained earnings equal to the firm's required rate of return on its common stock (Ke)?

If the company has the opportunity to earn a rate of return less than its cost of capital, but it will still generate a profit, should it make the investment? Why or why not?