measure Watts, given only Current in a single-phase AC system
From the datasheet you can see that there is sufficient isolation to support your needs.

However, whether it's safe for your depends on either the implementation of the board your bought, or the PCB you laid out. When including mains voltages and MCU/logic level circuitry on the same PCB you have to be very careful to ensure you have the correct spacing of tracks. 

I consider PCBs such as these (Ebay specials) to be quite dangerous as they have no solid mounting points or have very small safety spacing on tracks so are difficult and potentially dangerous to use.



A much safer sensor interface is to use a current transformer, again readily available and easy to connect to an Arduino A/D.



Here the mains is kept in it's rated cable and well isolate from your MCU/logic levels.

Since you are measuring a resistive load all you need to do is find the peak current flowing. From this you can find the RMS current and even assuming the mains voltage you'll get reasonably accurate results. For an Arduino based solution sensing only the current flow I'd suggest you find the zeros crossings (of the current waveform) and simply calculate the top of the sine wave current flow and trigger the A/D. Or you could take say 1kHz readings, and search for the highest current reading.   

Remember that if your load is reactive in any way you need to measure voltage/phase/current together to get accurate power readings. You could then follow the bouncing ball at OpenEnergyMonitor.