Because only true religion is from India and God has chosen only India. Your statement says it itself. Why only India, because only Indians were pious enough to invite God to take birth in the country. Everybody is a hindu, but some don't accept in out of their ego. If muslims did not come from manu, then from where did they come? the date palm tree of arabia?
Obviously Rama as avatar has to follow the dharma of humans and hence he prays most obviously to himself. need he pray to anyone else?
Hindu 'gods' are not assigned limited tasks, but the tasks are embodiment of various powers of the Supreme Brahman, which you may call as Rama, Krishna, Shiva, Shakti, Durga or any other name you please. the change in name does not affect the power