Slight rephrasing; there was an error in my previous argument.
The nickel forms cations. This repels the hydrogen cations, so the hydrogen cations go over to the neutral copper where there is less repulsion. The hydrogen ions, being positive charged, attract electron density from both the copper and nickel, but the nickel gives up electrons more readily, so the nickel pushes electron density through the copper, which then pushes electron density to the hydrogen ions.
As for the energy efficiency, I'll provide an example. Suppose you had fuel A with a molar mass of 100 g/mol and it produced 100 kJ of energy per mol that reacted. Suppose fuel B had a molar mass of 1000 g/mol and it produced 200 kJ of energy per mol that reacted. Now, the only reason fuel B has a higher enthalpy of combustion is because its molecules are larger than fuel A's molecules, so there are more bonds reforming. However, B is ten times as massive as A, yet it only produces twice as much energy as A. If A were of the same amount as B, i.e. we had 1000g of A and 1000g of B, you can see that A will produce more energy than B. Although we have different molar quantities of A and B, the masses of the atoms that make up these amounts of A and B are the same. So enthalpy per gram gives a better measurement of how much energy is released per atom and thus how efficient these fuels are.