APNAP rulings applied to world effects
APNAP doesn't factor in. APNAP is used when multiple players need to make choices simultaneously, and when stacking triggered abilities of multiple players. These questions are strictly about priority.

As the active player, you get priority after a spell resolves.


  116.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.


If you were to play a land then (a special action), you would get priority again.


  116.3c If a player has priority when he or she casts a spell, activates an ability, or takes a special action, that player receives priority afterward.


So the answers to both questions are yes.