Oh come on. This is a specific BT service that allows your home router to be used by the public (for a payment to BT, presumably the home owner gets a cheaper service or some return on the deal?). Should BT really enable the searching of non-SafeSearch material via such connections? Should Google really prevent BT from implementing this system?
What is it about extreme internet content that you think is so important that BT should support it being downloaded via their customers home routers without those customers knowledge? Or is it that schools use such a system to block extreme content - presumably you think that the dreggs of the internet are appropriate for schools to allow students to access easily?
Google's not stopping you searching for whatever extreme content you like they're just limiting their enablement of such searches in circumstances where those in control of the internet connection choose for it to be limited.
You get access to the wifi network on other routers. You don't get anything else in return - this is included in the cost of the bill.
You can phone them and get them to disable it on your router.
Their routers seem to have no QOS - one computer doing an update will kill internet for others in the house, presumable this is the same if other users are on the 'BT Openworld' wifi it shares.
That's not what the article says, it says they've outgrown their mission statement, which was to “organise the world’s information and make it universally accessible and useful”. Which makes sense, since they've expanded beyond information services.
Censoring wouldn't break the law, they're already doing that. And the blog post specifically mentions that it wasn't blocked using DNS but by a redirect from a Google server.
