Not reading real well today. Just noticed the OP called out the hard metal line, part 11. Sort of hard to understand how or why that would go bad. The vacuum valve, part 8, and the air pump, part 1, are common failures.

Maybe an o-ring failed?

If the metal pipe is occluded with carbon, that means air isn't blowing into it properly and more parts are probably bad.

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David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles