I guess one can begin by asking the question, 'What facts of reality give rise to the concept of investment?' Rand answers this in the OP's quote (in the lexicon): "nature requires time paid in advance..." That is, production is a linear process where value is continuously added from start to finish. In order to create a high value, one must spend the entire time required to produce it. Or, as Rand puts it: "This means that he is relying on a continuous process of production—which requires an uninterrupted flow of goods saved to fuel further and further production."
In order to start producing a value, man must either start from scratch, or if he already has existing value stored in money (gold), he can use the stored value as a starting point in production and start much further ahead. Thus, an investment is the name given to the act of using stored value to create more value. It's the initial "flow" of value that is required in the act of producing a higher value. This is why 'emerging markets' need investment to grow quickly. Notice how the American economy has reached a high level of production compared to other areas of the world, but the so called 'emerging markets' are catching up extremely quickly. This is because they have the advantage of using the capital of the more mature markets- capital that America had to create itself.
I hope that makes the concept of 'investment' clearer. It's the use of existing value as a starting point in order to create more value. How this applies to real estate investments is along the lines of what the OP thought in the beginning. The purchase of a house in order to live in it is NOT an investment. It's the consumption of capital because it's not a cash producing asset. At the very best it's a store of value (although I'm not even sure of that). On the other hand, purchasing real estate as a rental property IS an investment. You're committing your capital into a property with the expectation of using that property to receive cash from a renter. Another example is gold. Gold isn't an investment because it's not producing. It's just storing.
I now agree with you. Graham's reasoning is wrong, but I still believe that there is a valid differentiation and that the concept of speculation, as opposed to investment, is useful. Since investment is the process of committing stored value to gain a head start in the production of greater value, this rules out certain financial actions from being labeled 'investments.' For instance, buying a stock based on technical analysis is not an investment because it's contributing capital with the hope that, for reasons unrelated to production, the value of the purchased asset will rise.
Yes, it's still an investment because you're contributing your capital to the company by proxy. The amount of capital owned by the company hasn't changed, the ownership of it has. Now, instead of the seller's capital, it's your capital that is invested.
Once you think about investing the way Rand describes, you can see that buying bread isn't investing. Consider a man opening a business to produce shoes. Buying bread is necessary for his life, so in that sense it's necessary for production. However, once the bread has been purchased, the man is no better off in the creation of the business. The bread has not contributed anything to the flow of value (or 'flow of goods') that Rand describes. If however, the money for bread was used to help purchase the company headquarters, you could say that it was used such that the man was closer to opening the business. That would be an investment.
And just a final point on distinguishing investment from saving: Saving is accumulating value. Investing is contributing or arranging the accumulated value such that a higher level of production is possible.