It depends on which Wiccan Path you are looking at. Some have taken from the Celtic faith, Nordic faith, Eastern Faiths and even Native American Faiths. Every group will have different influences.
I think that the Druids were the High Priests of the ancient Celtic pagans. Wicca is inspired by Celtic paganism, yes. The Druids had a strictly oral tradition, which was mostly lost when the British conquered the Celts.
Not really. Wicca borrows bits and pieces from a variety of traditions and cultures, including Celtic Druidism, but its not terribly substantial. Wicca is far more directly influenced by Ceremonial Magic such as that practiced by the Golden Dawn, coupled with more general Romantic notions.
There are a few similarities, but they are fairly superficial. The Greater Sabbats commonly take their names from the Celtic Fire Festivals, although their meaning and celebration often differs immensely, for example.
Of course, some Wiccans draw upon Celtic culture more than others, but I'm presuming you're asking about Wicca in general.
First of all, respect to SweetNyjah, and the admission I am not a Wiccan. That said I've had Wiccan friends since the eighties and have read my star hawk and Margot Adler's Drawing Down the Moon and I can assure you both from anecdotal personal experience and from the books which have been published since Wicca began to be practiced in public that its sources are eclectic -- deliberately and unashamedly so.
There have been groups in Britain which called themselves druids at least since the eighteenth century. And to some extent these were almost certainly known by many British and American Wiccans. Gerald Gardner claimed to have been initiated into a Prue-existing Coven. Now while there has been SOME debate about that, he is generally regarded as a religious reformer among people sympathetic to Wicca, there has also been a suggestion that the high priestess of this cult was formerly a member of the Golden Dawn, which would have made it a more intellectual form of occultism than Family Tradition. FamTrad, as it is called for short, was cited by Leo Martello in his Witchcraft teachings -- and his family was Sicilian. Other writers whose books were influencing that kind of thinking at the time Gardner was working included Dr. Margaret Murray, an Egyptologist whose the Witch Cult of Western Europe was published late in her life and was discredited after her death, and Robert Graves, who several Mythographers on this list will get on my case if I don't at least say is problematic (he is not exactly a scholar though he was a well-trained one: he called most of this work poetry and it does make sense on that level). Wicca has diverse origins and people who wish it well would do well to celebrate them all.
Wicca is a modern invention of a British Civil Servant in the 1940s-50s who needed to make more money (borrowed from a 1930s fake religion). He took almost every mythology known to the Europeans, including some they borrowed from Egypt and mixed them all together to make up something that would sell books. The old Celtic Religion, is the Old Celtic Religion, as Norse Heathenry is Norse Heathenry, etc, etc, etc. "Wicca" is a hodgepodge that would be like mixing all of the Christian religions together. Imagine Catholic belief in the 'host" being mixed with the Mormon sacred undergarments, mixed with the Jehovah's witnesses denial of the cross, mixed with the Baptist believe in "once saved always saved", Mixed with the Worldwide Church of God's belief that the Britons are actually lost tribes of Israel, etc, etc, etc.
Celts, of which the Druids were the clergy-caste, had at most 4 high days, not 8. The Celts are polytheistic, unlike Wicca which is duo theistic or even monotheistic. The Celts were warriors, not "An it harm none" folks. Druids dressed up for ritual, rather than got naked.
It took 21 years of study to become a Druid, while you can find Wiccan high priestess who got there because they read one book and have the biggest living room of all the members of their coven......
actually the "Strictly oral tradition" was interrupted when the Romans killed a huge number of Druids at Yns Mona in Wales. the Britons are Celts as well. the British never conquered "The Celts" they periodically had bloody annexations of Ireland. The Celts were in a huge area of continental Europe as well as the British Isles. and no one can really answer this question definitively except to say Mr. Gardener developed Wicca from several sources less than 100 years ago and some Celtic traditions are part of it. as far as I know Wiccans are not Druids, they are a different group.
Wicca drew from a number of sources. Certain Celtic elements have been drawn in, either originally, or since then. However, some of the details that have been drawn in (especially originally) were from the "Druid Revival" that started back in the 1800s that, shall we say, lacked a grounding in any real Celtic scholarship. Unfortunately, there are still folks who erroneously claim that Wicca was the religion of the ancient Celts, that the Celts worshiped a potato goddess, etc.
Modern Noe-Druids and Wiccans started forming groups at similar times, so there is a certain amount of "cross-Hellenization" between modern groups. That said, Wicca is not based on the ancient Celtic beliefs terribly much.