My battery has some liquid spill on top and on the sides.
I didn't touch it, but I assume this is sulphuric acid leaking, and not any kind of oil.
Does sulphuric acid dissolve nitrile gloves? Could it be any other kind of acid?
After removing the battery (hopefully with my skin still intact), my intention was to pour maybe 20 litres/5 gallons of tap water slowly to rinse away any acid that might now be eating the plate under the battery, but Paulster's recommendation to use baking soda is clearly better, since it would neutralize the acid in place, without risking that the acid, no matter how diluted, would still be too acidic and would eat away on its way out of the car, which would be nasty enough to cause the metal to rust, but also to seriously damage any tire it may touch.
Hence, I assume, it's a good idea to rinse the baking soda with a hose (pipes are still winterized in our area), and not just with a few pots. Ideas welcome.
I'll ask for one more hint.
The battery is in the picture above. (It was quite a bit more "moist" two days ago. Now it appears to be drying.) It is supposedly sealed. Could it be that under these two covers there are screw-tops that simply need to be tightened, making the battery salvageable? The battery so far works just fine.
Thanks to a pointer provided by rustyx, the chemical resistance of nitrile gloves to Concentrated Sulphuric Acid is "Poor" and that to Diluted Sulphuric Acid is Excellent. The question now is whether the sulphuric acid in batteries (at 37%?) is nearer to concentrated or to diluted.