I only tried the first one, and it is immediately bad. In the second move, Re1 and Bxg2 are also mate. Playing mate-in-3 should not be "incorrect", it is completely ridiculous.
In #1 the listed third move could be played as the second move (both mate on move three)
In #4 I'd prefer an intermezzo capture with check and follow up check before playing the listed move 6 because that way your can also keep an extra piece.