me da muchos energías = Not Correct Because "Energía" is a female noun. Try to remember that in spanish, Noun must match in number and gender with adjectives.
So in this case the right way is : Mucha Energía. (A singular female adjective plus a female noun)
Muchas energías is not possible because "Energía" is a non countable noun. You wont listen... "Dame una, tres o mil energías). You give all the energy or nothing.