1. What is the purpose of the circuit C-M-C?
Use-value. You start off with one commodity you want little, and end up with another commodity of the same value which you want more.
2. What is the purpose of the circuit M-C-M'?
To expand value. You end up with the same use-value as you started with - money - but with more value.
3. Where do profits come from?
The fact that there is a commodity whose consumption creates extra value, namely labour-power. When the buyer of labour-power 'consumes' it, that means that her or she sets the worker to labour. The labour creates new value in excess of the value of the labour-power, which is determined by the average 'living wage' of the time and place.
4. Why say labour-power is bought and sold, rather than just labour?
Marx writes in chapter 19: 'That which comes directly face to face with the possessor of money on the market, is in fact not labour, but the labourer. What the latter sells is his labour-power. As soon as his labour actually begins, it has already ceased to belong to him; it can therefore no longer be sold by him'. In capitalist production, workers do not own their own labour. They sell their labour-power for a pittance sufficient to enable them to continue to be workers, and in return the capitalists gain control over the whole social process of producing new wealth, which they can organise and reorganise so as to maximise the new value produced.
5. What's wrong with the idea that profits come from the capitalist's 'abstinence' in investing his wealth in production rather than consuming it straight off?
This approach:
a. Explains only interest - not profit - if it explains anything at all;
b. If taken seriously, implies that profit rates will be high in countries where people are impatient, and low in countries where they are patient!
c. Ignores the fact that the capitalist investing millions in production has no desire at all to spend his whole fortune in one spree, any more than people in general desire to eat all their week's dinners on Monday. The worker waiting to be paid at the end of the month is the one more likely to be 'abstaining'.
d. Further ignores the fact that the capitalist class as a whole could not consume its whole wealth in one spree, even if they wanted to. How could they eat all the factories?
e. Fundamentally, gives no real explanation of economic facts, but only an attempted sentimental apology for them. See how patient the capitalist must be! Surely the dear man deserves some reward...
6. Are workers paid a fair wage? If so, how can we talk about exploitation?
By the standards of the wages system, they may well be paid a fair wage - though a lot of workers are not, since they are paid less than the value of their labour-power. But the wages system is exploitative whether the wage is fair or unfair. Marx, I think, wants to emphasise that exploitation is not a matter of the capitalists grabbing bigger slices of a fixed cake than the workers. It is a social relation in which the workers produce wealth and power for capital and poverty and subordination for themselves. The fact that the capitalist makes gains 'free', by 'pieces of good luck', is exploitative because those gains increase the mass of wealth and power bearing down on the workers.
7. What is wrong with the academic economists' definition of capital? 'Capital, in sum, is any previously produced input or asset of a business firm or any other producer' (Baumol).
Capital is a social relation, not a thing. A computer or a sewing machine or a desk which you have at home is not capital. Exactly the same object in a factory or office is capital. See Marx, 'Wage Labour and Capital'.