If you control “Harpies’ Hunting Ground” on your side of the field, because it is a Field Spell Card, its effects apply to both players. When either player Normal Summons or Special Summons a “Harpie Lady” or “Harpie Lady Sisters” to the field, the controller of that newly-Summoned monster is the one who selects 1 Spell or Trap Card and destroys it.
You can chain to the effect of “Harpies’ Hunting Ground” that destroys 1 Spell or Trap Card.
The effect of “Harpies’ Hunting Ground” that increases ATK and DEF is applied to all face-up Winged Beast-Type monsters on the field, including your opponent’s, because it is a Field Spell Card.