Are stock dividends exclusively part of earnings? Or are there cases when companies pay dividends despite zero or low earnings?
In the end it comes out of earnings, but the earnings don't have to be made that financial year. So yes you can pay dividends despite negative, zero or low earnings in a specific year. This can be a strategic consideration of the company called dividend continuity.
This is based on German Law (§ 150 AktG), but should be applicable elsewhere as well.
Cash dividends are paid from the company's cash on hand. It doesn't matter where that money comes from. You might have earned it that year, previous years, or (rarely and foolishly) borrowed it or retained it from a stock offering, etc.
A cash dividend is funds or money paid to stockholders generally as part of the corporation's current earnings or accumulated profits.