Why should we worship statues of Lord Buddha? 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).