Capacitor

I don't know but it is long...until the capacitor itself broken and cannot store engery anymore.

Farads = coulombs per volt.

Energy = 1/2 farads times the square of the voltage.

Capacitor

On a DC generator and providing a way to stop the charge from being fed back(e.g. relay or diode), yes but it'll be pricy for any time length. On AC don't know. Maby I missed the creation of AC current accumulating capacitors. Can't keep up on everything these days. S.M.

What sort and size of generator are we talking of?

Without giving some basic information you really can't expect an answer.

Yep. Ever heard of an uninterruptible power supply, a.k.a. an UPS? Try googling that one. Electricity from anything can be stored in a capacitor. Try googling that first.

Yes, it can be stored in a capacitor, though if the generator is AC the power would need to be converted to DC via a diode or some other means. For how long depends on the type of capacitor and how it is stored (dry air, dust free, etc., to prevent gradual dissipation).

I used to work with CRTs. I always had to be careful around a bare CRT sitting on a storage rack because a CRT can act like a capacitor and store a tremendous charge. If it hadn't been properly discharged, and I accidentally touched the anode button, I could get a nasty shock as the CRT discharged through me. BIG ouch.

positive half of the sine wave...in this case.

There are UPS systems which only use capacitor banks to hold the load in the event of a disturbance.

If the guy is talking about just hooking up capacitors willy-nilly, like they are plug and play...well...he's a goober.