(1) What does GDP measure?

It measures C+I+G+NX, collectively known as aggregate demand.  All goods produced within the national economy that are bought, either by domestic consumers or consumers abroad.

(2) Why does it need to grow?

Inevitably we develop ways to produce more with less through innovation.  If fewer employees are needed at a company because of a boost in productivity, then "spare capacity" results, and it follows that the economy must expand in order to absorb factors which are idle.  Or, in short: "There is more to be done."

(3) Does the need for GDP growth outweigh any other policy goal?

In my opinion, no.  The need to develop alternative energy sources, in order to avoid the effects of global warming, dependency on an increasingly-scarce source, and other related issues, says, to me, that it is worth sacrificing some GDP growth in order to place the economy on solid ground for the future.  But, with that in mind, it should also be apparent that it is only a temporary sacrifice and might well result in a stronger economy, with more consistent GDP growth, in the future.

Be nice to America. Or we'll bring democracy to your country.