(my bold)
1) According to the licence T&Cs, no. (Although I would hope CaRT would be reasonable if you told them you needed to go to a water point or fuel supplier, before returning to where you are moored. )
2) Minimum of 28 days from a notice being attached to the boat and probably (a lot) longer. However, the time to take action, if you feel that is a real possibility, is NOW, to take legal advice and be ready to apply for judicial review of the revocation as soon as it occurs. If it gets to court on a Section 8 (assuming CaRT adopt their usual course of obtaining a court order), it's too late: there is no licence in force, and the case is open and shut. There are several precedents for this.
3) After receiving the Section 8 notice, you have the 28 days to leave CaRT waters.
4) No idea, but I'd assume they would if asked. CaRT reserve the right to pass on personal information to anyone who has reason to require it, and I'd assume the EA do likewise.
Section 8 of the British Waterways Act 1983 would only come into play if the licence is revoked. Section 13 of the 1971 Act, although always quoted along with Section 8 of the 1973 Act, has no additional effect.. It applies to "houseboats", as defined in the 1971 Act.