I cant watch the video at work (work blocks it) so cant comment on most of your questions at this stage.....but the engine in the Mk5 GTI has a timing belt, not a chain. So you can rule that out.
Water pumps are a common failure in the Mk5 too. I'll watch the video tonight and see if i can help further - but there are some VW trained mechanics on here who might be able to help also.
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