The aircraft is effectively territory of the state of registration.
So far as I am aware this is not the case. I know of no provision in the Chicago Convention (or any other Convention) which makes such a provision. Certainly UK legislation is applied to foreign registered aircraft
The local police has not, I say again to make it clear: HAS NOT got the right to enter any aircraft under a foreign flag unless allowed by the Commander.
Again this is not the case. Article 16 of the Chicago Convention provides that "The appropriate authorities of each of the contracting States shall have the right, without unreasonable delay, to search aircraft of the other contracting States on landing or departure, and to inspect the certificates and other documents prescribed by this Convention." I know that the UK police have the power/right to enter foreign registered in specified circumstances under article 144 of the Air Navigation Order and under the Railways and Transport Safety Act.