Can I read out this 10V load cell with the 5V OpenScale board?
Addressing your questions in reverse order.


3) From the documentation for the OpenScale board, I note the following.


  "When the report rate is above 500ms OpenScale will automatically turn off the power to the load cell between readings. This saves power and limits the amount of localized heating of the strain gauges."


Until correctly configured, the board will not apply power, and even when it does, a 500ms pulse may not be enough time for the DMM to give a stable reading.
2) The design of the load cell is passive, using a circuit called the Wheatstone bridge consisting of four resistors. It will perform perfectly fine at a lower voltage, but your measurements may vary slightly from the manufacturer's specifications (it is likely they test their product during manufacture at 10 volts).
1) Based on the design of the OpenScale, I would not recommend using an external power source. The voltage supplied to the load cell is also used as the reference voltage for the analogue to digital converter in the HX711 ASIC. By using another power source you will reduce measurement accuracy and may damage the IC. Unless your load cell has a very low resistance (measure between the 'red' and 'green' wires or equivalent) of less than 50 ohms or so, you should have no problem driving it with the OpenScale. The specifications of the load cell in your link give a resistance of 700 ohms which should work well.