I have a large gap between the windshield and the windshield cowel cover. The rubber is no more, as it has dried and torn.
Also, the plastic lid that gives access to the battery is slightly shifted and has small gaps too.
It should rain and snow soon.Is there a danger of short circuiting the battery? Or causing even fire? Do I have to remove the battery until I replace the windshield cowel cover?

 

I recommend getting this https://www.ecstuning.com/b-assemble...1132751210kt2/

Idk if you will actually run into any issues with your damaged cowl cover, but it would be smart to repair it. I think you only need a 10mm socket to complete the job

 

I am planning to repair it. But for now, I'm just worried that snow or rain might get into the battery compartment and cause a short circuit or even a fire. Not because of the crack on the driver's side cowl cover, but since there is no rubber (mounting strip) anymore on the passenger side cowl cover, where the battery is, as shown on the first image. Or am I talking nonsense and it's not designed to be waterproof anyway?

 

It's fine, that area is not designed to be waterproof, and a little water won't harm the battery. A good rule of thumb is "anything under the hood that stops working when it gets wet needed fixing anyway".

That said, the cowl kit linked to above is not very expensive and it's relatively easy to replace. You'll probably need to buy or rent a wiper arm puller.

 

I got some water in my battery bay under a heavy rain. I just replaced that one side on my R58 JCW. Some people have reported after driving though massive rain they got water in through the cabin filter and on the floor.

For a quick fix i got self tapping short screws and wedged it in place tight. Then got the part fixed same day at work.