You can pump water uphill back into reservoirs so that you can use it to generate hydro-electricity later https://en.wikipedia.org/wiki/Ffestiniog_Power_Station

Yes. Desalination or hydrogen separation via electrolysis

Both uses are productive, one generates fresh water, the other can be a form of energy storage.

Both are extremely energy intensive for the yield, making them unprofitable, but are extremely useful things to do with a glut of electricity.

There is, but you have to set it up and link it with the central control system of your grid, similarly to how power generators have an automatic generation control to balance the network.

Yes there is. So consumers (with the right kind of smart meters) are paid to use energy and we are slowly moving from pilot plan into small scale production of hydrogen. But there’s nowhere near enough and the grid will literally fry itself unless producers stop pumping more onto the grid (during windy and sunny days, in areas with high penetration of intermittent production.

Central heating