Mirrors don't work in the way you're suggesting because they don't provide enough of a shift in frequency in the energy they rebound (though they would act as an effective shade). For active cooling strategies, what you want is a material that can take the infrared frequencies from a heatpump, and shift them to the specific frequencies that make it hard for the atmostphere to absorb (similar to the use of phosphors in lighting for the visible spectrum).

Edit: I clearly didn't read this particular article closely enough, and the process they're measuring is actually a passive cooling system, which shows the material, or at least it's shade to be cooler than ambient temps. You could still use this material in conjunction with simple radiators to get better performance from a heat pump though.

Yes.

The sun can hit the roof all day and it will not heat a normal house...so many layers in between and the heat will not reach below.

IMO it's just a matter of time before we use the sun to offset its effects on homes and offices. A super sunny day gives us a lot of power we could use to cool what the sun is heating. They coincide perfectly for a lot of hours.

This is completely false. An attic that's heated up to 130+* will have a significant impact on the temperature of the house it's attached to unless you use an uncommonly ridiculous amount of insulation. This is why things like attic fans are so effective in reducing AC load...