Not just fixed but most engineers design with UL standards so while they advertise maximum output they're all most efficient somewhere around 80% their maximum.

The batteries help the grid because they can maintain a minimum demand the power plants need and compensate for any excess demand that would tax the grid infrastructure.

I've never tested a generator, are they all producing pure sine waves?

Unless its a Chevy Volt. That was a really interesting car in many ways, but they kneecapped fuel efficiency by eating transformer losses twice instead of licensing Toyota patents.