Why should we worship Lord Buddha statues with flowers, lights and food, even when we know Lord Buddha is not alive and does not exist? Did Lord Buddha instruct us to do so or is there any other reason?
I am not sure we should worship statues itself as that would be some sort of idolatry. Buddhists worship Buddha, and statue or other image is just symbol, something that bring into our memory good qualities of Buddha. It's mindfulness of Buddha. Statue is a symbol, and symbol is communication which states about its subject, Buddha in our case. Thus, showing respect before statue should be directed to Buddha as Jewel, and not to statue. Mindfulness and respect to the Saint and Teacher is good action.
Btw, Buddha is not disappeared, he stated that he will remain in his Teaching (Dharma).
Thanissaro says in many places that the act of respect develops hand-in-hand with learning the path:
In their eyes, the religious attitude of respect is needed for any philosophical understanding to grow. And as far as they're concerned, there's no conflict between the two. In fact, they're mutually reinforcing.
The veneration of statues with flowers and so on should be a natural expression of your development of the path. The act of putting flowers next to a statue doesn't save anyone or develop anything, but it's an expression of your faith that what the Buddha taught is really worth learning:
Respect is the attitude you develop toward the things that matter in life.
No one should worship any Statue, in death bed Lord Buddha says not to build any statue of him.
More over He had been saying this all his life that his path is the path of practice not worship.
Now comes your Question why should we worship him ?
Once a king denied to worship a statue, then swami vivekananda asked him to spit on one his fathers portrait, as a result kind was angry.
So we should always keep in mind that the most important thing is to focus our minds, some may need help to keep it focused maybe some statue and some may need breathing techniques, some doesn't need anything, they just sit totally blank, As everything came out of nothing, nothingness is god, having a controlled & focused mind in nothing is all we need to do.
The true Buddha is the Eternal Buddha revealed in the Lotus Sutra. It is not a normal human being. The statue serves as a tool for remembrance, but it's actually an inferior symbol, because it depicts the bodily form of the Buddha. A scroll with written characters is better. A Sutra (text) is more similar to the true Buddha-body than a statue of Siddharta Gautama. The true Buddha-body cannot be expressed or depicted so it expediently reveals itself in ways that are understandable to our feeble minds - such as "infinite buddha" (amitabha) etc. Since the true buddha is formless, it cannot be depicted or potrayed. But since it compassionately discloses itself to ignorant beings, it allows to be depicted in such a way. It's simply a useful device. It's dangerous though, because someone might cling to that body and believe a Buddha's body can decay, break or die. That's not possible according to the Nirvana Sutra - the Buddha's body is permanent & eternal. - To answer your question: what we really worship is the Buddha-nature that is present in every sentient and even insentient being. It's in you & me too.
Buddha is a Sanskrit word meaning knowledge. Thus a statue of Buddha is a personification of knowledge. Buddhists do not pray to Knowledge (Buddha statue). They venerate knowledge because 'knowledge is power'; they pursuit knowledge.
Theists hope to get power by praying. Teaching of Lord Buddha (Budda is a statue) is for practice, diligent strenous practice, to get knowledge.
See definition of Buddha and Buddhism in Oxford Dictionaries.
Lets say the Buddha was alive today and you offered Dana to the Buddha. But what if the Buddha does not accept it? Will you still not get the merits for your good intentions and the effort you put into preparing the Dana for the Buddha? It's about the quality of your thoughts throughout the time you spent on it.
No one worshiping Buddha in India, We just ignite candle only . And so if we gonna experiencing just observe you'll see Buddha's statue, his face there's en lighted spirit, you'll not find with other gods, only Buddha's eyes are closed and peaceful spirit on face. Peaceful atmosphere you'll feel. Worshiping means bribe from devotee and want praise through chants; but we don't have to worship Buddha to achieve peace. He just beyond concept of god and religion. You can meditate next Buddha's statue.
The Buddha never asked to be worshiped, he only asked that we use the Dhamma and Vinaya as a guide to cessation. Respect and veneration of the Buddha are wonderful, in that they engender a respect for their Buddha, Dhamma and Sangha, but valuing the Buddha as anything more than a teacher will likely lead to attachment and stress/suffering.
The Buddha shined a lamp onto an individual path, one without an idol - where the cessation of stress/suffering is realisable in the here and now, generally with him as a guide.
In the Kalama Sutta he denies the absolute validity of all speculation, no matter what this speculation is grounded in, rather asking each one of us to search out and find out the knowledge found in the Dhamma for ourselves!