Galvanic Corrosion of Copper, Aluminum, and ENIG Plating
Will there be a galvanic corrosion issue with the ENIG and copper or
  aluminum?


Aluminum is is a class of it's own and does not like copper. There is some risk of putting aluminum directly on copper, and it is smart to start questioning this. 

Corrosion occurs when there is a ionic solution (most likely moisture) with two metals that are not in the same galvanic series. The galvanic series that your materials might be most exposed to is something like tap water, but it can be different depending on the environment. The idea is to match the potentials closely, the further apart the metals are, the greater risk for corrosion.


Source: The effects of electroless nickel coatings on the galvanic corrosion of other metals

With Aluminum on the top at around -1100mV, nickel in the middle at ~-300mV and copper at the bottom +80mV. So sandwiching nickel between the two lowers the potential between the two and risk for corrosion.

If the aluminum comes into contact with copper there won't be corrosion necessarily, there needs to be water or some other solution to kick the ions around, so try and keep moisture out as a first rule, but there is always some moisture in the air. 

The second thing would be to plate the aluminum with nickel (I've heard chrome isn't as good for heatsinks). An enig coating on the PCB side might be ok also, as long as it doesn't get too scratched. Or even better, an ENIG coating on both.

This article shows what can happen on a micro scale with an ENIG coating on aluminum, it needs to be continuous or there can be problems. 


  Will there be an issue with the copper bar and aluminum heat sink?


Yes copper on aluminum is bad, with a coating of ENIG there will be less corrosion.