This is a very interesting thread, especially since a good deal of reading I've done recently has involved exactly this question. The piece which I will quote from is a book by D.T. Suzuki called "Zen and Japanese Culture". I know it may be boring to read quotes from a book, but Suzuki addressed much of what is being discussed here. The difference? He has extensive footnotes for every bit of it...which should settle much of the idle speculation on this topic.
To begin with, the original question asked, "How connected is Tao with Buddhism and Confucianism?" On this, D.T. Suzuki writes the following:
"Zen united itself to a great extent with Taoist beliefs and practices and with the Confucian teaching of morality, but it did not affect the cultural life of the people so much as it did in Japan."
Bearing in mind that his book was actually written specifically on the subject of Zen, Suzuki goes on later to remark:
"I will not enter into too much detail in regard to the interrelationship of Zen with Confucianism and Taoism in China. Suffice it to state here that Zen is, in fact, the Chinese way of responding to Indian thought as represented by Buddhism and that, this being so, Zen, as it developed in the Tang and later flourished in the Sung, could be nothing else but a reflection of Chinese mentality."
"Zen acquired its practicalness from Confucianism, whereas Confucianism absorbed through the teaching of Zen the Indian habit of abstract speculation and finally succeeded in giving a metaphysical foundation to the teaching of Confucius and his followers."
going on...
"It was thus natural for the Zen monks to become propagators of Confucianism in addition to being Buddhists. Strictly speaking, Zen has no philosophy of its own... Zen Buddhists are sometimes Confucianists, sometimes Taoists, or even Shintoists."
"There are two original currents in Chinese thought, Confucianism and pure Taoism, that is, the Taoism not colored by popular beliefs and superstitions. Confucianism represents the positivism of Chinese mentality, whereas Taoism represents its mystic and speculative trends. When Buddhism was brought to China...(A.D. 64), it found a real associate in the thought of Lao-Tzu and Chuang-Tzu. In the beginning, Buddhism was not much active in Chinese thought; its adherents occupied themselves mostly with translating its texts into Chinese, and the people did not know exactly how to take it into their system of thoughts and beliefs."
Suzuki briefly explains that the Chinese were intrigued by these new ideas, though he adds that
"while they could not clearly grasp the idea of sunyata, 'emptiness', they found it somewhat akin to the Lao-Tzuan idea of wu, 'nothingness'."
Frankly, I don't feel like scanning the whole chapter to provide a zillion pages of quotations. I would highly recommend reading the book, instead.
Suzuki, in summary, shows that beginning in general vicinity of the turn to the "A.D." years, Buddhism's introduction to the culture of China from India had a profound effect upon the native systems of thought, which were Taoism and Confucianism. During the many hundreds of years that passed while China was absorbing these new ideas, the line between them sometimes became much more blurry than one might be compelled to think. The introduction of Buddhism into China had an ultimate effect of revitalizing the Chinese systems of thought, which drew from Buddhism many kindred lines of speculation. Many Masters during those days were Taoists that studied Zen, as well. There were many Buddhists that were steeped in Confucian ideology.
What we know today as these three seperate traditions have actually all had a profound impact upon each other, as in their continuing development, they all tended to draw this or that from each other, strengthening and enriching each tradition.
