It is just like all the rivers are mixing in the ocean. Origin and end is same. The same ocean water evaporates, rainfall occurs, it passes through various rivers and joins the ocean after some period.
Buddhism is from India. Taoism and Confucianism from China. Over the course of many years Taoism and Buddhism have merged to a high degree in China. Some people say they have merged completely. I don't know about that, but in some regions or specific Buddhist sites it may be the case. Buddhism, Taoism and Confucianism are all philosophies which may be said to promote wisdom and the cultivation of traits like humility and temperance. Buddhism focuses on things like universal friendliness, compassion and the pursuit of enlightenment. Taoism allegedly has no set rules. It is a subtle wisdom but I'd say not at all incompatible with Buddhism. Confucianism does not address enlightenment or reincarnation. I would describe it as a way of life based on sensibility, right action and conscientiousness.
The main trait between Buddhism, Taoism and Confucianism is that they are spiritual philosophies that do not worship any particular god or gods. (Except for Buddhism in some sects, which I think is completely defeating the point, anyway..) Buddha was an Indian Prince (then known as Siddhartha) who shed his worldly possessions and attained enlightenment. Buddhism believes that life is full of suffering that must be overcome. Buddhists believe in enlightenment (well, some do.) Many follow the eight fold path.
Taoism explores very abstract concepts and focuses on things like yin and yang, and the intrinsic duality of nature. Zen Buddhism (a very philosophical, abstract form of Buddhism) shares many similarities with Taoism in this way. Taoism focuses on the nature of the whole and how it is often composed of two opposing factors.
Confucianism, like Taoism, was developed in China. It is based off of the teachings of Confucius, a ancient philosopher who once had a school (one amongst many) where he dispersed his teachings. Confucianism believes in filial piety (children's' loyalty to their parents) and sacrificing the individual for sake of the group. It's a rather narrow-minded belief system, I think. But it illuminates a lot about Asian culture, especially regarding the Chinese.
Completely different, although they all have the coincidental characteristic of being non-theistic worldviews.
Buddhist and Confucian ethics have many similarities, partly due to Confucian influence on Chinese and East-Asian Buddhism, the most notable of which is respect for parents and teachers.
(Philosophical) Daoism has the similarity with Buddhism of being non-violent and anti-materialistic.
Buddhism originated in what is now Northern India and Nepal, and Confucianism and Daoism in China.
They are entirely independent philosophical/religious systems with their own histories and unique understandings of the world. However, in many places, such as China and Taiwan, people will believe in a mixture of Buddhist, Confucian and Daoist beliefs, which constitute Chinese folk religion.
I think yes, all the three share a lot of characteristics especially in the field of the rational thinking, giving respectable place to doubt, meditation and the ways of learning as well as of teaching.
Confucius was said to have beaten an old beggar on the side of the road one day, telling him that he was old and should go die so he would not burden society any longer.
The Buddha, on the other hand taught non-violence, and required himself and all his monks to beg for their food.
Taoism involves a lot of ancestor worship if I recall, but its not something I've studied as much as the first two.