Calculate voltage, current, and power for each element
...is 10mA is the same throughout all the elements That is correct.

V2=(10mA)(1k)= 100V You mean 10 mA * 10 k = 100 V answer is correct though

The power of V3, think about that for a moment.

If you take a voltage source like V3 and it delivers power to a load like a resistor, what direction is the current flowing? What direction is the current flowing in this circuit? Is it the same direction or the opposite direction.

So does V3 deliver power (like when there is only a load resistor) or does it absorb power?

Why do you assume that the sum of all powers must be zero? Does "passive convention" apply here? I do see sources that can deliver and absorb power so..

How about simply calculating the voltage across source I1, that's simple. You already know the current as well so the power can be easily calculated.