Inning/warm ups

Question: In high school baseball and softball, following the top half of the first inning, when does the home team half inning begin? When umpire says play ball; when the third out is recorded?
Answer: The half inning ends and the new half inning starts when the final third out occurs. (BB – Rule 2, Sec. 20, Art. 1 & 2; SB – Rule 2, Sec. 31)

Question: Following the completion of a half inning, how many warm up pitches is the pitcher allowed (9, 8, or 5)?
Answer: At the beginning of each half inning following the first inning, pitchers are permitted to have no more than five throws, completed within one minute, timed from the third out of the prior half inning. (BB – Rule 6, Sec. 2, Art. 2(c); SB – Rule 6, Sec. 2, Art. 5)