Being a shareholder, you have a share in the ownership of the company. You make money when the value of the company increases. This is especially true with Amazon, which does not pay dividends (a share of profits to investors).
For a static, non-growing company, you can treat its value as equivalent to a bond paying as much interest as that company pays in dividends.
Company can have value w/o giving out money if it's expected that it will give out more money tomorrow; but it can't be expected to keep that way forever.
A stable, static company that brings $0 profit is worth $0 if it's intended to keep running that way; or worth $assets-$liabilities if it's intended to be stopped and dismantled.
That's true. However, the value of the company will only increase if it develops profitable business units or it accumulates salable assets. In both cases this represents delayed profit, not nonexistent profit.
Their businesses are profitable, they just aren't booking profits. Odds are eventually they'll simply use free cash to buy back shares instead of reinvesting it. Which is why Amazon attracts quite a few very sophisticated long-term investors, and why they command a relatively high valuation.
Well, it's possible to have free cash without being profitable on paper. For instance, remember that depreciation is a major expense for capitalised assets (such as fulfillment centres, data centres, computer equipment, real estate, etc.) but isn't actually a hard cash expense, just a formal expense. The hard cash expense came at the time that the investment was made, i.e. when the data centre or what have you was actually bought and paid for.
So, the difference between that "virtual" expense and actual cash is one accounting category that free cash can come from. There are others.
Forever seems a bit long. But as long as Amazon feels it can reinvest above some threshold, it is prudent to continue investing instead of making profits.
