Missing access hole covers in the stiffening plate - I don't think that's a big deal. My car was like that when I got it 2 years ago (and still is) and I'm not concerned. Very doubtful that it would be related to your alternator problem.

When the alternator on my '01 3.0i went out (VALEO 120 Amp alt), the charging light would come and go intermittently for a very short window until it died completely. Turned out this was the more-worn of the two brushes finally wearing down enough to lose contact with the slip ring.

On my alternator, the brushes assembly is part of the Voltage Regulator. At the time, I could not wait to get all the parts (bearings, slip rings, etc.) for a more complete rebuild, so I just replaced the Voltage Regulator. That's where I would start looking if I were you. If that is the problem, clearly neither rain nor open access ports had anything to do with the failure. It's just normal wear. Mine went at around 170k miles, which I think is typical for those cars/alternators.

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2001 X5 3.0i, 203k miles, AT, owned since 2014