See Appendix II in the NCAA rule book on record keeping. It covers pretty much all of what you're asking:
NCAA Appendix II wrote:Faceoff—The standard of faceoff statistics is to award the faceoff to the
faceoff specialist (when his team gains possession of the ball), regardless
of whether he actually gained possession himself. A faceoff should
be awarded to a team only when it gets a clear offensive or defensive
opportunity out of the play.
Note: As stated in Appendix II-h, ground balls should be awarded in
faceoff play.
A.R. 9. A1 faces off for his team. He obtains the ball in the faceoff situation but the
ball is immediately checked away. B1 picks up the ground ball and his team maintains
possession of the ball. STATISTICAL RULING: Credit faceoff to Team B.
A.R. 10. A1 controls the ball on the faceoff, retreats into the defensive half of the field,
closely guarded, and throws the ball away. STATISTICAL RULING: If Team B can
obtain possession of the ball and keep it, credit Team B with the faceoff. Similarly, if
Team A subsequently obtains possession of the ball and keeps it, credit Team A with the
faceoff.
A.R. 11. Same situation as A.R. 10, but A1 advances the ball to his offensive half of the
field, closely guarded, and throws the ball away. STATISTICAL RULING: Same as
A.R. 10.
A.R. 12. The ball goes out of bounds on the faceoff before a team obtains possession
of the ball. STATISTICAL RULING: Credit the team that is awarded the ball on the
out-of-bounds play with a faceoff. If neither team is awarded the ball out of bounds, delay
the crediting of the faceoff until the subsequent re-face is concluded.
A.R. 13. Before either team can obtain the faceoff, a player on either team is charged with
a foul. STATISTICAL RULING: Credit the offended team with the faceoff, if one
team gets the ball. In the case of a double foul, or any other violation requiring a re-face
of the ball, wait to credit the faceoff until the play is complete.
A.R. 14. A goal is scored near the end of the period. STATISTICAL RULING: If
there is no subsequent faceoff, no faceoff can be credited statistically. If a faceoff occurs,
award the faceoff as judgment allows by determining the possession (or something close
to it) when the period ends.
A.R. 15. A period ends in an uneven situation such that there will be no faceoff to start
the next period. STATISTICAL RULING: Do not award a faceoff.
A.R. 16. If there should be an extra faceoff for any reason, credit the faceoff according
to the preceding rules.