GFCIs only trip if the difference between the line and neutral currents is greater than 5 mA. You have current leaking to ground somewhere, and since it is intermittent and only occurs when you plug in your lighting, that is where the problem is. Wipe down all you lighting cords, sockets, inside the socket mounting box, etc. with a damp paper towel followed by a dry towel. Salt creep isn't always visible, it can be a very thin layer (you can usually feel it, though). Make sure the lamp cords are not touching the aquarium anywhere, esp. near the top, as that can also lead to leakage. If your lighting fixture is metal, wipe it down as well. I'd also wipe down any sockets/power strips/timers, esp. near the receptacle (unplugged, of course). That should solve your problem.
The reason your AC unit is turning brown is because you have too much current flowing through it. It is unrelated to your GFCI tripping UNLESS something inside the unit has gotten hot enough to degrade the insulation of the wires, conductors, etc.
