I am going to answer your question with a preface defining my terms. First I am going to assume by Wiccan, you mean Witchcraft generally, and Gardnerian Wicca as one representative of such. You probably just didn’t know there was a distinction, which is normal when you are starting out.
1) Yes there was a somewhat sudden witchcraft revival in the 1950’s when in England the last of the witchcraft laws was repealed and was replaced by the fraudulent mediums act. This act was repealed due to the emergence of Spiritualism and their quest for religious freedom in England. Witch enthusiasts like Gerald Gardner watched this legislation closely and came out of the broom closet in the news very publicly.
Although Gardner’s form of witchcraft was initiatory only, he wrote several books about it and initiated a number of other witch enthusiasts who were in show business of one kind or another. He and his initiates wrote a number of books and did a number of TV appearances about witchcraft. And many derivative books on the same have been written opening up many of the outer court practices of Wicca to the world and to solitaries. There were also people who against the wishes of their elders published the Wiccan book of shadows despite their oaths, I know of at least 4 such instances of the BOS being published. At the same time, many people who had been practicing as witches secretly, continued to keep it under wraps.
2) Over the last 60 years the popularity of both witchcraft and paganism has increased and there are tons of books sold even on your major bookstore shelves. The political battles have not ceased as Witches, Druids, Pagans and others have sought out religious freedoms/freedom of practice. Platforms like listservs in the 80’s-90’s, and blogging and social networks in the 2000’s-2010’s have expanded people’s awareness. Furthermore, movies and tv shows spread even more awareness.
3) Gardnerian witchcraft (Wiccan) practice and many other forms of traditional witchcraft do focus in on a female and a male spirit or deity. Often its a horned or antlered god of both dark and light underworld and sun, and a moon goddess. However, witchcraft as a practice rather than a religion proper has many expressions secular/no gods, many gods, one god, two gods, one goddess, etc.
3) Gardner believed in reincarnation, that people stop off in a nice place that he and other people in groups like his called the Summerland and then are reborn on this earth. His maxim was once a witch always a witch and he had a ritual to be reincarnated into the same coven again. It seems as though he believes this is what happened to him and he wrote a few novels that seem to be semi-past life-autobiographical. This understanding of the afterlife is shared among many witchcraft lines, but not all. Some don’t believe in an after life, others believe in heaven and hell, others don’t believe in reincarnation but instead in a pagan afterlife.
4) As for proof of things working, it depends on what you count as proof. However, most witches keep doing it because it is working for them and some of them have personal experience of talking with their passed on friends and ancestors.
Thank you for the excellent question!