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Runner on 3rd less than 2 outs, batter hits a routine fly ball deep enough for the runner to tag up. Outfielder misses it. The runner advancing home will be scored as due to error or advanced by batter?

Somewhat similar, full bases less than 2 outs. Hard grounder to shortstop who fields it but overthrows to 1st. Will runner advancing home be scored due to error or advanced by batter?

Thanks again.

In the first situation, if you think the ball was deep enough to tag up and score and the fielder committed an error, then score it as a sac fly with an error (In Play | More... | Sac Fly with Error).

In the second situation, since the run would have scored even if the out had been recorded, then the runners are advanced by the batter.

In both cases, the batter should get an RBI.