Stock in a company is equity. You own a slice of the company. If the company pays dividends, you are entitled to a portion of its future earnings.

Yes, that's essentially correct. And that's why stocks can plunge and lose practically all (or all) their value relatively quickly, as happened to General Motors and many banking stocks in 2008, for example.

Edit: To clarify, even when a company pays dividends which holding the stock entitles you to you are speculating the company will continue to pay, or be able to pay, which is why you continue to hold the stock. This is why stocks are risky -- they have no guaranteed value (or backing) and can crash theoretically at anytime.

Not at all. A stock represents a share of a company's earnings, which has real fundamental value. There are bubbles and random swings, but at the end of the day, a stock is worth something like the present value of future dividends. (Even for a non-dividend-paying stock - the idea being that eventually the company will mature and start paying a dividend.)

Similarly to jerf, I think if you point this out to someone "in the know", and dig deep enough, they won't get mad, but it'll turn out that it's "really complicated" and "you wouldn't understand unless you were heavily involved". It happened at least once, and I wouldn't be surprised if this was common.

A stock should be backed by all the assets of a company, shouldn't it?

A stock is backed by companies' performance, I think.