Example, using Inferno Overdrive (fire type Z-Move) during the rain, will the damage be reduced, or still stay the same (175 damage) ?
They are effected "normally" by weather, so No.
Even if a status Z-Move fails, it still applies its Z-Power effect. Z-Moves are affected normally by Powder and weather. Weather-changing moves turned into Z-Moves (except Defog) will disappear as usual during heavy rain, extremely harsh sunlight, and a mysterious air current, but will apply their Z-Power effects regardless.
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