He's genuinely dead set on getting Greenland.

Yep. And he's said that military force is an option. Which would be required, because the new leader of Greenland is saying "no" quite definitively.

So could he do it? Congress has let the Executive get away with a lot for the past 10-15 years in terms of military interventions. Could they stop him? I think that resolution/authorization for use of military force is still in place long after 9/11 has ceased to be relevant. If so, the Executive could argue that they still have the authority to order attacks or invasions.

I think the third term would be unachievable. Each state has to put the candidates on their ballots, and there are enough non-Felon states that would refuse based on the Constitution. CA, NY, IL, CO, and several others would never do it. So he couldn't hope to receive enough votes, assuming he could get the Rep nomination.

And they couldn't amend the Constitution that quickly to repeal the term limit (again, assuming they would have the votes in the states to get that done anyway, which they wouldn't).