If a Muslim commits adultery while living in a non Islamic country (eg: the UK) is the punishment execution?

I suppose there are multiple angles to this question: 1. Can a sharia court from outside the country of residence be used? 2. Can punishment be carried out in a foreign country (where execution is not permitted) 3. Can punishment be carried out in a foreign country (where execution is permitted, eg the USA) 4. Can a sharia court in the country of residence be used? (Are they allowed, even if not officially 'courts' in the host country) 5. Can Muslims commit adultery with impunity in foreign countries if they live there and the host country is not Islamic and permits adultery?