How to check if something is mains earth grounded?

You can use the continuity function on your multimeter for this, connect one end to the ground of the power outlet and the other to any other point that you know to be grounded. Not sure if there are any safety issues involved but I've done similar with my bench power supply and scope and it worked well.

Socket tester checks the sockets are correctly wired with indicator lights that accurately denote no neutral, live and earth reversed, live and neutral reversed and no earth.