Sell electricity at spot prices, give consumers access to that spot price, and you'll see a lot of demand flatten simply through natural market forces.
Where I live, I pay five times more for electricity between peak hours of 2pm and 8pm than I do between off-peak hours of 10pm-8am. (The remaining hours are priced at a medium level.) This has changed my behaviour, in that I now tend to wait until bedtime before switching on the clothes dryer and dishwasher.
No, although the current system is pretty tame. The electric company can turn your electric water heater or air conditioner (depending on geography and utility) off for 15 minutes at a time, and in return you get a credit on your electric bill. Its opt in.
Yes, industrial plants will turn off production (for instance at an aluminum smelting plant) in relation to the frequency of the grid. Grid frequency decreases slightly when demand starts outpacing "supply."
That frequency change used to be a natural reaction from the generators.
I wonder whether they create that signal artificially with electronics these days, or if it's still a natural consequence of the mechanics of the spinning generators they run in power stations?