Feeding energy to the power grid
Yes, it works. The grid itself provides the frequency and voltage reference.

The inverter is programmed to feed current into its connection with the grid, in a direction that feeds power in, and a magntitude that looks like a negative resistance.

Imagine something as simple as a resistor connected to the grid, a 3kW kettle of roughly \$20\Omega\$ resistance for instance. When the instantaneous grid voltage is 100v, it draws 5A, when it's 300v, it draws 15A. 

Now with some clever electronics, you could create a load that sensed the instantaneous voltage, and drew that amount of current. That would look like a resistor at its terminals. Those exist, and they're called power factor corrected power supplies. 

You can do exactly the same thing, and sense the grid voltage, but this time feed current in rather than draw current. That's how a grid-tie inverter sends power into the grid in a well controlled fashion. 

Any commercial inverter will have protection on its output so that in the event of grid disconnection, it won't generate too much output voltage.

The arrangements around money changing hands for this are mired in political issues, with incentives and tarrifs in the driving seat.