From the sounds of it, it's your alternator belt. When you go through a big puddle water splashes up around the engine, if the alternator belt gets wet it will slip and obviously won't be charging the battery. That explains the battery light coming on. Petrols aren't good with water, because they rely on a spark to ignite the fuel, if it gets damp there will be no spark and the fuel will not ignite, but there are 4 plugs (maybe 3 if you've got a 1.0 corsa), if one goes your car will just perform crap, if 2 or more goes you'll be lucky if the engine stays running. If that happens just let it dry out for a few hours and it will be fine, but while they are damp they wont spark and the engine could stop.
Diesels on the other hand compress the fuel and it ignites because it is under such a high pressure, it's only if water gets sucked into the air intake that you can damage a diesel, if water gets into the air intake look out lol.
I think thats right anyway lol.
EDIT: Just seen the ebay item you posted and that would probably work, but it's a lot of money to stop a couple of lights coming on. Does the car actually do anything different when they come on? If not then I wouldn't worry too much about it, as long as your brake fluid is topped up and alternator belt is in good shape I can't see there's anything to worry about. Always easier to avoid or slow down through puddles
