You CAN leave it plugged in all night but you only need to run the block heater for 3 hours or so, even in the coldest weather. So if you have a heavy duty timer you can use that if you like to save electricity. No harm will be done by running the heater all night.

To check if it's running, open the hood, put your head down over the engine and listen carefully. You should hear a hissing or singing noise rather like when an electric kettle is starting up.

I ALWAYS unplug the heater before starting simply to avoid the problem of driving away in a forgetful mood with the cord still connected to the power plug, with obvious side effects about to happen in 0.5 to 1 second. Don't ask me how I know this!!!!!!

PS you DO have synthetic engine oil?