Remember to read your casebook, not just the rule.
For the puck out of play, the face off is located based on who caused the puck to go out of play. "Last play" faceoffs are determined by which team's actions caused the stoppage. In your case, the defending team caused the stoppage by deflecting the puck, and since it was inside his defending zone, the faceoff is at the nearest end-zone faceoff spot to where the puck went out.
For the hand pass, it's defined in Situation 4 of the casebook
https://www.usahockeyrulebook.com/page/show/1085021-handling-puck-with-hands