It will be important to keep an eye on power dissipation. The specs say 1W. Your stated max load will be okay, based on I * I * R. (Or .8 * .8 * .242 ohm, using an 'ON' resistance found in the table.)
Nevertheless, it's wise to put your fingers on the device while testing operation. 1 W is too hot to hold, which will tell you the device is at risk of frying.
Keep in mind that a bulb has lower resistance at turn-on when cool, compared to when the filament has become hot.
Re Q 1.
Though it's not specified on the datasheet, the device when off should draw only miniscule current. It would not make sense for it to draw substantial current, seeing it's designed for battery powered projects.
Re Q 2.
Perhaps not all load currents go through the drain terminal. If they did then drain current will be the sum of all load currents going through the device.
So it may be relevant to examine source current too, in case you have it carrying one or more load currents.