You could buy a new battery online, but it is probably a similar price to a new or very good condition used macbook. The soda will also accelerate oxidation of the integrated circuits, so your keyboard and memory will start to go soon. I would recommend just buying a new one.
Make sure the flash is turned on. If your camera still doesn't flash even though the option is enabled, your bulb could have burned out and the whole pop-up assembly will need to be replaced. If this still doesn't solve the problem, your motherboard may have a broken wire or capacitor (which charges the bulb).
This might be an EGR valve. The EGR is responsible an emissions control part located behind the intake in line to the engine. You can take it out and soak it in carb or fuel injector cleaner then scrub the muck out with an old tooth brush. Wear gloves when you do this as the chemicals and the carbon buildup have been known to be carcinogenic. After reassembling, if there is still a loss of power, check your spark plugs and replace them. If that still doesn't work you may need O2 sensors somewhere, or coilovers (which are the wires that connect from the alternator to the spark plugs.) If any of these are bad, then a piston could lose combustion. Also pour two or three bottles of good quality fuel injector cleaner into your gas tank when you are low on gas and run the engine. This will clean out any carbon buildup in the entire fuel system. Autozone will be able to give you the codes though and you can google them, but from all the symptoms, it is my guess that your EGR valve is gunked up. Good luck buddy!
Yes, you can open the camera up and check the connections. If they are connected well and all other parts are working, you probably need a new zoom assembly, which has the power button as well. Alternatively you can zoom with your fingers on screen by moving them toward each other or away from each other. If the camera does not zoom by either method (I.E. the dial by the power button, nor the touch screen input), then check the lens apparatus itself. There may be dirt or something, or a loose cable somewhere. If everything looks good it might be broken and need to be replaced. Hope this helps Sophia!