The stalker couldn't have possibly taken a human head in a box as hand luggage on an airplane, as this would have been detected on the luggage scanner.
The garage has an electronic up-and-over door, but no other exit points at all (hence the mystery of the disappearing "skeleton man"). However, this is illegal in Britain; no electronic doors can be installed if there are no ordinary exit-doors which can be opened with a key, precisely so no-one can be trapped within due to electrical failure.
Emma Lazarus' body is kept in a coffin at her home, shortly after her murder:
1) The body would have been taken away for post mortem examination (amongst others showing the brain tumour this episode in the end centers about) and forensic tests.
2) Assuming a post mortem examination had been done, then, when the head was cut off and stolen by the stalker, the neck wouldn't show trachea and esophagus anymore (as it still does in this episode), as these are removed during a post mortem.