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1) That assumption is not particularly valid. I would estimate closer to half that, but never mind.

2) Actually answering your question.

There are two seperate concepts to keep track of.
Power (measured in watts)
and energy (measured in watt hours).

You could refer to the total amount of 'juice' stored in a battery, which is more technically the total power in the battery and is thus measured in watts. It is meaningless to talk about whether the total power stored in a battery is 'per hour'. Whether you drain your battery quickly or slowly it contains the same power.

You could talk about the ability of the battery to deliver charge quickly, this is then the energy consumption of whatever the battery controls. This is measured in watt hours (Wh), which are simply equal to the average power (in watts) times the number of hours.

So if you run a device at 250 W for 1 hour, you use 250 Wh of power.
If you use a 1 W device for 250 hours, you use 250 Wh of power.

tl;dr 'power used per hour is meaningless, you want energy per hour, which can be worked out by simply turning that 250 W into 250 Wh.

As for cost, you are correct that you would be paying 5c per hour assuming that is the cost of energy in your area.

You can get devices that measure the power and energy used by a device, such as described here http://www.choice.com.au/reviews-and-tests/household/energy-and-water/saving-energy/power-meters-review-and-compare.aspx

Any questions?