Yes, all air transport operations into the Cayman Islands are subject to regulation under the UK’s Air Navigation (Overseas Territories) Order, AN(OT)O, and in particular Article 135 which provides that all foreign registered aircraft operating into the territory for valuable consideration be licensed to do so by the UK Secretary of State. This authorization has [...]

Once the operation in not for ‘gainful consideration’ a permit is not required. Response to Part 91 Operators

Once the CAACI is in receipt of all required documents (see non-scheduled checklist) an operating permit can be issued within 3 days.

All documents submitted to the CAACI must either be in English; or dually translated with English as a language or the foreign language to be accompanied by a notarized English translation.

Yes, an approved ground handler is required to operate into the Cayman Islands. The Cayman Islands Airports Authority issues a list of all licensed handlers.

Aircraft shall comply with Standard 2.1.10.1 and 1.2.5.2.3 of Annex 1 of the Chicago Convention when operating Air Transport Operations into the territory. Below is a summary of the key elements of this standard: A Contracting State, having issued pilot licenses, shall not permit the holders thereof to act as pilot of an aircraft engaged [...]

Yes, this list can be found on the CAACI website.