Divorce and children

Divorce final 4/2016. Divorce decree states I claim one of the children, she claims the other. Joint legal and physical custody with 3 nights/week with me and 4 nights/week with her.
Questions:
1. Do I input info into turbo tax for child I DON'T claim as dependent?
2. For child I DO claim as dependent, what do I put for turbotax question of how long she lived with me?  I ask because I input "all year" and it's suggesting I should receive head of household benefit which I think is incorrect