Wires with constant power and increasing voltage

My question is in the attached image.
Before going right at it, I thought it would be best to clarify a few details.

Ohm’s Law only shows that current and potential are linearly related, correct? So R is constant in the case of a material that follows Ohm’s Law (metal conductors for the most part, right?). But regardless of the material, isn’t resistivity and as a result resistance of an object w/ constant length and surface also a constant? Or does it vary with current/potential? Isn’t V = IR the definition of resistance? Do all three variables change in no particular pattern for materials that do not follow Ohm’s Law?

Also, does heating in a wire depend on BOTH resistance and current? Are there any other factors?

Now, to the attached question, I am assuming that the wire follows Ohm’s Law (is that a reasonable assumption?). I’ve circled the correct answer, but cannot quite understand why C and E are wrong. We know P is constant, and so is R if it follows Ohm’s Law (once again, would R be constant if the material did not obey Ohm’s Law?). Thus b is false since resistance of the wires stays the same. And even if it did change, P = V2/R, so resistance would not decrease. Also, isn’t insulation related to resistance? Assuming constant resistance, this property does not change, so d is wrong.

Now, I know P = IV, and if V increases then I decreases. But if V= IR and R is a constant, if V increases doesn’t I increases as well? What am I missing here? Also, isn’t the IR drop simple V (V=IR). If V increases, then doesn’t IR as well?

Just so you know, we were told all answers but a are false. Any comments on why and could you possibly critique my reasoning as well? Thanks!

Attached Images
File Type: png Screen Shot 2014-02-26 at 4.13.58 PM.png (61.9 KB)

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