It's partially rent-seeking by NR (or whatever subsidiary it is controls station lets these days) and partially retailers exploiting a captive audience. They don't have to, and several examples such as Boots and Waitrose have been cited upthread, but most of them choose to.
Yes, that's right. VAT is chargeable on hot food and on food consumed "on the premises" whether hot or cold. You will therefore see Greggs charge extra to cover the VAT on items that are not deemed "hot food" when you eat in. (For reasons out of scope of this post, their pasties, sausage rolls, and similar are not deemed "hot food" and therefore attract this surcharge.)
VAT is also chargeable on "luxury food" such as confectionery, chocolate-coated biscuits (but not chocolate chip cookies), ice cream, and crisps.
It is clear from
VAT Notice 709/1, paragraph 3.2, that seating areas provided for the general public at railway stations do not constitute part of a catering premises, as long as they are not restricted to customers of one or more catering businesses. Cold food served to consume in such a location should not have VAT charged, unless it is one of the "luxury" food types as mentioned earlier. I'm not familiar with the location so cannot say with certainty whether this rule applies or not.
Yes.