You may be confusing the Empire (gone) with the Commonwealth — still alive and kicking. SA and India are part of the Commonwealth. A subset of the Commonwealth, the “Commonwealth Realm” comprises nations that recognize Queen Elizabeth II as the reigning constitutional monarch (i.e. Head of State). Canada, Australia, New Zealand, Britain, and a dozen other nations are members of the Realm.
Recently, a “movement” began to create a “Commonwealth Union”, which would be a free-trade bloc, a visa-free travel area (like the EU), have a common foreign policy, etc. This idea hasn’t gone too far (yet); but, it is, as I said, an option for Britain.
Not possible. The homosexual lobby would not allow those countries to keep their sodomy laws.