The wires connected to pins 2 and 10 do not connect through to any other pins, they are used only to turn the relay "on" or "off" - switching between normally closed and normally open positions.
When the relay is "off", meaning no power is applied to the coil, pins 1 & 4, 6 & 5, 11 & 8 are connected.
When the relay is "on", meaning power is applied to the coil, pins 1 & 3, 6 & 7, 11 & 9 are connected.
What you connect to pins 1, 3, 4, 5, 6, 7, 8, 9, 11 is up to you.
As an example, what you could do is connect pin 1 to the neutral wire of a pump, then connect pin 3 to the neutral wire of a cord connected to your house power, and connect pin 4 to the neutral wire coming out of your power inverter.
Thus, when you have power at your house, pins 1 and 3 are connected meaning your pump get's it's power from the house.
When the power goes out, pins 1 and 4 are connected so the pump gets it's power from your power inverter.
You could do similar for the hot wire, etc.
You have the right idea for wiring the Inverter switch.
Cut one of the wires on the switch, then connect a new wire from one end of that cut wire to pin 5 or 6, and another wire from the other end of the cut wire to the other pin.
This will turn the inverter on when your power goes out.
As mtndavid said, if you are not 100% comfortable doing this and you don't think you have a full grasp of the wiring, you are better off not attempting it because incorrect wiring could be quite harmfull...
