How are the elements of Buddhist Cosmology (31 planes of existence, hungry
ghosts/shades, angry deities, etc.) confirmed?
There are those that are born natural Mediums. Their ability to detect outside the normal human frequency, like many animals, is heightened. Their E.S.P., or extra sensory perception, extends beyond the normal physical senses. They simply are able to tune into a frequency band greater than most. Some can see ghosts; some can only hear them, while other Mediums are shown visions and guidance in their mind's eye, or "third eye" from the beyond. These are the John Edwards of the world, or the crime solving specialists.....
Are there writings of recent gurus in the past 50 years or so, confirming,
questioning or analyzing the elements of this cosmology in the light of modern
science and their own experience?
Refer Edgar Cayce.
Other than faith in the ancient texts, is there any other basis for modern
Buddhists to believe in Buddhist Cosmology? If so, what is that basis?
The multiverse (or meta-universe) is the hypothetical set of infinite or finite possible universes (including the Universe we consistently experience) that together comprise everything that exists: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them. The various universes within the multiverse are also called "parallel universes" or "alternate universes".
The structure of the multiverse, the nature of each universe within it and the relationships among the various constituent universes, depend on the specific multiverse hypothesis considered. Multiple universes have been hypothesized in cosmology, physics, astronomy, religion, philosophy, transpersonal psychology, and fiction, particularly in science fiction and fantasy. In these contexts, parallel universes are also called "alternate universes", "quantum universes", "interpenetrating dimensions", "parallel dimensions", "parallel worlds", "alternate realities", "alternate timelines", and "dimensional planes", among other names.