1. Yes, profit and loss accrue to a person for his superior foresight in anticipating the state of the market that is actually realized in the future. It is a pure residual after accounting for the payments for productive contributions made by the person. The theoretical treatment of these factors takes two steps.
First, economists identify four categories of generating income from an entrepreneur investing in his production process. He earns wage income from the productivity of labor services he provides. He earns interest income from capital funding he provides. He earns quasi-wages from leadership skill in organizing factors of production in the most productive combinations. He earns profit (suffers losses) from superior (inferior) foresight.
Second, interest income has four sources. The rate of time preference generates a positive pure rate of interest. The particular degree of uncertainty of the project invested in generates an uncertainty premium (inaccurately called a risk premium in finance). Cantillon effects from a change in the money relation. (For example, if the central bank generates a monetary inflation, the prices of some goods will rise to a greater extent than the prices of other goods and the prices of some goods will rise sooner and that of other goods later. The rate of return on investment in the former lines of production will be greater than in the later lines of production.) Changes in the purchasing power of money that are unanticipated will enhance the rate of return when the PPM goes down (with price inflation, interest rates are higher) and detract from the rate of the return when the PPM goes up (with price deflation, interest rates are lower).
So, all the sources except the first involve anticipating uncertainty and therefore have a profit and loss element to them.
2. Economists define these terms to facilitate understanding of certain theoretical aspects of human action. For economists, saving refers to the restriction of consumption while investment refers to the acquisition of goods (made possible by restricting consumption) with the intention of increasing the value of consumption in the future by more than that given up in the present (in others words to earn a rate of return). So, the basic distinction for economists is between “consumption” (acquiring goods for the purpose of obtaining the subjective value from attaining consumptive ends in the present) and “saving-investing” (acquisition of goods for the purpose of earning a rate of return. Obviously, a person could acquire some goods to satisfy both motives.
Economists further distinguish between “saving-investing” done to earn greater subjective value in the future directly (e.g., storing canned peaches in one’s pantry in August to eat in December) and “saving-investing” to earn a monetary rate of return (and, then use the monetary gain to obtain goods of greater consumptive value in the future). For the purpose of understanding the market economy, the later type of saving-investing is more important and so, this is what economists are usually referring to when they talk about saving-investing. Murray Rothbard calls this “capitalist” saving-investing.
With all of this as background, we can address your situation. First, the only difference between saving and investing is that they are two steps to a single action. They are never done separately. (Let me remind you that this is just the way in which economists define the terms.) Whether or not the acquisition and holding of money is an investment depends on the motive of the person holding the money. If the person is striving to earn a monetary gain from the appreciation of money relative to a good he intends to buy (at the then lower price), then it is an investment. Normally, money holding, however, is not capitalist saving-investing. Most of the time, people hold money to help them deal with the uncertainty of the future. If so, money holding is, at most the former type of saving-investing. Rothbard denies that money holding is saving at all, however, because it involve no sacrifice of present subjective value.
Second, economists do not use the terms “saving” and “investing” to refer to save and risky investments. We just refer to differing degrees of uncertainty that different investments entail.