Several questions
This Hoovermatic is unusual in that it has two pumps for the wash tub - it is the only one I know of to offer the water recirculation feature.
To answer your questions:
Empty Wash tub
Make sure that the bent hose emerging from the back of the machine is in the sink and that the sink is free draining. Turn the "power drain" control to drain. With the machine turned on (but the impeller in the wash tub NOT running) lower the spinner lid to start it and the tub should then drain as it seems that the spinner motor is the one which empties the tub. Do not run the impeller with the wash tub lid raised while the machine is emptying our you will get wet mighty quick!
The white lever you refer to is for the automatic rinse and can also be used to fill the wash tube with water. There should be a second hose emerging from the back of the machine with a faucet connection on it. Connect this to the faucet, lift the "lever" up and to the left so that it is over the wash tub and turn on faucet until the correct water level is achieved - there should be a mark on the side of the tub. Switch off faucet and return the "lever" to its resting position.
Just as a side point, it would probably be worth running the faucet before connecting the hose so that you have hottest water possible going into the tub.
These machines are notorious for tangling the clothes so, contrary to the many videos you will see on youtube, the impeller should NOT be running when you put the clothes into the tub. Push the clothes in down the edge of the tub. It will take a 6lb load
Once the wash has completed put the clothes into the spinner. The purpose of the rubber mat is to go on top of the clothes to prevent small items such as socks being flung out of the spin can during the spinning process.
Take the bent hose and hang it over the side of the wash tub. With the right hand control set at the other position from automatic lower the lid and the soapy water extracted from the clothes can be returned to the tub to use again - it may need a little top up with both water and a little detergent.
Once the initial spin is complete, return the bent hose to the sink again making sure the sink is running freely. Swivel the white "lever" over to the right so the end of it is over the spin can. With the other hose connected to the faucet, turn on the water (if you have a mixer faucet you can regulate the temperature, starting off warm and finishing off cold) turn the rinse control to automatic and lower the spinner lid. The spinner will cycle on and off and in theory you carry on this way til the water from the bent pipe runs clear. At this point turn off the faucet and turn the rinse control to the other position and spin until the water stops coming out of the bent pipe.
Two points to note:
This automatic rinse uses a lot of water and is not particularly effective so, if you have sensitive skin you my find it better to rinse in the sink after the first spin (returning soapy water to the wash tub is complete) is complete.
The final spin can be up to four minutes long but the clothes will be very creased - more so than an automatic washer, so you may want to trade off the drying performance against the creasing of the clothes.
Al