All of the below assume you are talking about a regular wet lead-acid battery. If you are talking about other types, please ignore!
Ok, back to the question: Well you can, a TINY pinch can help dissolve sulphation when the battery is next charged and warms up. However a SMALL pinch only (it will neutralise some of the acid as well as hopefully removing some of the sulphation, converting it to sodium sulphate).
EDTA or epsom Salts tend to be worth considering if you are going to put something in your battery. With both, dissolve in a small amount of water around a teaspoon per cell (for typical car battery). Do NOT just plonk in the cell as epson salts especially do not dissolve well in acid - but dissolve ok in water - especially if hot.
If you Google for "battery desulphation" you will find other ideas if that is your problem - if you do not have a sulphated battery, then I wonder why you want to add caustic soda.
Baking soda mixed with water. and if this is like on your car battery put some Vaseline on it to keep it from coming back.
No you cant. Baking soda actually neutralises sulphuric acid . So you are left with only water in your battery. It may also damage the cells inside. But you can clean the outside of your battery with baking soda diluted in a water.
Jump the car from another car battery or hook a charger to the battery.
You can get a new battery, you can jump start the car with jumper cables and another car with a charged battery. You can also put a battery charger on your battery to give it a charge.
If the battery has more cranking amps than the recommended battery and will fit into the battery carrier box the answer is yes.
Is there power to the starter "S" terminal? What car?
If it is stronger than 0.5 molar (Mdm^-3), 2% per mass, it should be labbeled with the caustic symbol: http://upload.wikimedia.org/wikipedia/commons/a/a1/GHS-pictogram-acid.svg.
Disconnect negative cable first from old battery and connect it last when installing new battery.
No, it will do nothing
yes
No
Yes