The premonition of Carole Davies can be explained in terms of what I call congenital or ancestral memory. It is memory that is transferred to an embryo from its mother’s brain during gestation. Caroles mother or grandmother or great grandmother may have experienced the trauma of a collapsing building and her brain must have recorded the picture of the scene and the sensations of sound and vibration preceding it as a high priority reference. The memory was transferred from generation to generation and when Carole felt the sounds and vibrations before the museum collapsed, the picture appeared before her and she knew what to do.
As for feeling the presence or arrival of people, animals etc. such phenomena can be explained in terms of thermal radiation. All living and nonliving bodies emit thermal radiation all the time which makes it possible to take infra-red pictures. Thermal imaging can be done from great distances: the big bang experiment did it from billions of miles away. It is possible that some or all living bodies emit a thermal signature that is detected and identified by other specially gifted people.
Infrared signaling is commonly used in remote control devices and a system of protocols in UHF transmission of cell phones gets the voice and even picture across great distances. Why can’t a thermal protocol allow some specially gifted people to communicate over short distances?
For further reading refer to chapter on Islam and psychology in Islam for the Perverted and the concluding paragraph of Alternatives