If I play Phoebe while my opponent has a Dunsparce with "Mysterious Nest" Ability in play, do my Pokemon VMAX's attacks calculate Weakness if applicable or not?
The term "any effects" does not include effects that alter Weakness and Resistance. So Phoebe does not allow you to ignore Mysterious Nest's effect.
If I have Hiding Energy or Snow Leaf Badge attached to my Active Pokemon, would my opponent's Leafeon VMAX's "Grass Knot" attack do any damage to it or not? If yes, would "Phoebe" remove the effect of Hiding Energy or Snow Leaf Badge for the damage calculation of "Grass Knot"?
The effects of Hiding Energy and Snow Leaf Badge are not blocking any damage from the attacking Pokemon, they are changing the stats of the Pokemon they are attached to. So they are not really affecting the damage done by Grass Knot; it is still 60x the Retreat Cost, but the Retreat Cost is now effectively zero. And since those cards are not affecting the damage being done (they're only affecting the Retreat Cost), Phoebe will not help it do more damage.
