watt vs watt-hour.

An 800 watt solar system would generate about 5 kwh per day if setup fairly optimally. ~~5 kwh is a pretty typical laptop battery capacity.~~ 50-100wh is typical for a laptop battery.

Yes in principle to male plug, no to 240V unless the inverter sees a frequency to sync to. They won't power anything during a power outage that requires the whole electrical installation to be set up for it so you don't leak power to the outside and fry a lineman. Also that inverter attaches to one phase only which means that its power won't even reach 2/3rds of your circuits. It does make the power meter go backwards though which is the point.

That said, ideally you're using Wieland plugs and not Schuko so you won't have exposed prongs. The VDE certified Schuko for feeding in up to 800W though and that's exactly the amount parliament said doesn't require a permit or even talking to your utility. If you're doing everything new going with Wieland is the sane choice those outlets don't cost a fortune, if it's an existing installation though a) your landlord might not like it and b) electricians will demand more in travel costs than the outlet is worth.

The inverter is a device that converts the DC power from the solar panel to the AC power that homes are wired for.