I'm not defending Monarchy in any way, but it's his job to care about the Swedish populace. That he hasn't been elected to this position doesn't mean that he does not fulfill his job, so I would assume that at least he is better informed than the random person on the street.
Nah, he's detached from the Government and has no formal power at all. He is however a very public person, and pretty much never offers any dissenting views from the government.
A king is normally the head of state (1), so it would be the equivalent to the president of a country denouncing the the strategy of the government (and with it criticizing the head of government).
The main difference between a king and a president is that, with a president, if he/she is corrupt or incompetent you can remove it. With a monarch your are stuck for life.
In my opinion, the greatest virtue of democracy is not the power to choose who govern you, but the power to remove it from power peacefully. Historically that is pretty remarkable. Of course, in the case of Sweden, the king has a very limited power. The point is, it's not a random person.
A difference is that when asked loaded questions like this reported did, he can’t just not answer. ‘People died because of this policy’ what is he going to say? He’s not going to go into some statistics debate to show another point of view, he’s going to say that yes, that’s terrible.