Example 1 is a bit tricky for me, only because I think it's difficult for a scorer to tell the difference between a CF that is intentionally throwing home versus one that has misplayed a throw to second. Especially with no one on base, I would not assume that it was an intentional throw home. I would assume it was a misplayed attempt to throw to second and would award an error. Maybe if the player were well in and well away from center so that it was obviously a deliberate throw to the plate.
But "throwing to the wrong base" is explicitly called out as not an error. The MLB Rulebook has a couple of comments on rule 9.12(a)(1). One is quoted below. (My emphasis)
The Official Scorer shall not score mental mistakes or misjudgments as errors unless a specific rule prescribes otherwise. A
fielder’s mental mistake that leads to a physical misplay—
such as throwing the ball into the stands or rolling the ball to
the pitcher’s mound, mistakenly believing there to be three
outs, and thereby allowing a runner or runners to advance—
shall not be considered a mental mistake for purposes of this
rule and the Official Scorer shall charge a fielder committing
such a mistake with an error. The Official Scorer shall not
charge an error if the pitcher fails to cover first base on a play,
thereby allowing a batter-runner to reach first base safely. The
Official Scorer shall not charge an error to a fielder who incorrectly throws to the wrong base on a play.
The second scenario is clearer to me. Except for the fact that the fielder ran the ball to the wrong base rather than threw it, the spirit seems the same. There was no physical misplay, so no error.
I would assume a hit in the second scenario, and in the first if I were able to tell that the throw was intentional.