Clarification of cards in King of Tokyo
Is it every turn of the game (my assumption) or every turn of that player?


You are right. Notice that Mimic reads At the start of your turn, while Monster Batteries reads At the start of each turn. Interpreting the cards literally also makes the batteries a card that might be worth buying. :)


  My rationale on this (seeing as it is a "keep" card) is that you can replenish the stock of energy cubes in successive turns to receive more of the 2:1 bonus. Is this correct?


Being a Keep-card does not imbue it with more rules than are stated on the card. The only time you can put energy cubes on it is when you buy it. So you better have a fair number to make it worth your while.