The ball was dead as soon the ejection occurred:
Rule: 5.10(g)
Quote:
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The umpire in chief shall call "Time"_(g) When an umpire orders a player or any other person removed from the playing field.
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Also, if I remember correctly, the batter/runner was between first and second when the ejection occurred. Thus, he was not legally entitled to second, as he had not touched it, and therefore he remained at first base.
As for the play at home, I thought the plate umpire made the correct call. Even if he didn't, which I believe he did, the catcher had no reason to go off like that.