OBR, 13-15 Babe Ruth.

One out, B4 hits in B3 spot, K.
We skipped B3 and went to B5.

Correct or incorrect rulling?

Thanks

Did the defense appeal properly?

If not, OK - play on.

If they did: B3 would be declared out. B4's K would be nullified and B4 would bat again.

The defense can "ignore" it if they wish (usually because it is to their advantage). If it were me I'd ignore it in this case.

Depends. When was the infraction brought to the umpire's attention? If the infraction was brought to the umps attention before a pitch to the next batter, then B3 is called out for batting out of order and B4 bats his proper turn. If a pitch had been thrown to the batter after B4 had struck out, then B5 would be the proper batter and B3 would be skipped.

Defense caught it before the first pitch to B3.