Dangerous Power Supply
There is a good chance that there isn't anything wrong with the power supply.  But it will require more investigation on your part.

1) The AC Mains input terminals L &amp; N should NOT be connected to any of the output terminals.

2) The Earth terminal is most likely connected to the EMI filter capacitors that provide filtering on the AC Mains terminals.  You need to connect that Earth terminal to your metal chassis and to the Earth lead on the incoming AC Mains cable.  Also note that the metal case of the power supply must also be connected to Earth. That is normally done just by mounting the power supply to your metal chassis.

A little bit of history here: Where I come from (Canada), it is not legal to rely upon a mounting screw to be the only ground connection.  You can have a mounting screw that is part of the a ground connection but there must be another ground connection that is not used for mounting something else.

That applies to PC boards as well.  You can ground your EMI filter network to the metal power supply enclosure with one of the PCB mounting screws BUT that ground connection must not be the only place where the ground connection is located.  The power supply manufacturer must also supply a separate ground terminal.

Which they have done.

Finally, regarding your observation that the power supply 0V DC output is also connected to the Earth terminal: that is just fine.  For example, if you look at the power supply inside most personal computers, you will often find that the 0V DC wires are all connected to Earth.  There isn't anything wrong about this.

Having the 0V DC line connected to Earth may not be what you want and it indeed might cause you problems.  If that is the case, purchase a power supply that is completely floating with respect to Earth.  But it's not a defect if the OV line is in fact connected to Earth.