Question: If I host the domain for my UK business on one of these (and say it is a generic .com - not a .co.uk domain), will it influence my google.co.uk SERP ranking massively ?
I am not an expert, but my understanding is that it would have some effect (worse than UK hosting, presumably better than outside EU), but I doubt very much. Faster hosting should have a positive effect, too.
Webmaster tools?
Related: I host a org.uk site in the States which ranks well for relevant searches. It's a tourist site in the UK so I'm only really interested in UK traffic.
How would Google know my .com site is UK based?