Can a player use Moonlit Hill stadium's effect to discard a Basic Psychic energy from their hand even if there are no damage counters on any of their Pokemon?
No, the Psychic energy discard is a cost in order to do the effect of healing.
Source: TPCi Rules Team (2024-02-15)

Relevant cards

Note: All applicable cards may not be listed below.
SV45_81
SV45_81