I think that was just silly. Nothing actually happened in Greenland. His whole thing is about slowing China down. That explains Venezuela, Iran, and a lot of the price-rising tariffs are explained by wanting to choke Russia's oil and gas revenues, which also has the secondary effect of hitting China.

Somebody, in a conversation of which there will be no record, told him it was a good idea, telling him it would be quick, he would be lauded as a hero, there would be vast mineral riches, etc. This person wanted to break up NATO, but this wasn't part of the sales pitch, I imagine.

Reportedly, Rare earth minerals.

Almost everyone's asking the same question regardless of what they think's going on inside Trump's head. The two most coherent answers I've seen are "to soothe his narcissistic injury from being told he can't" and "feels entitled to it because NATO", you will note neither of these was his stated reason, and all of this is still catastrophically poor judgment on his part.