Both 1 and 2 are correct.
Political equality of citizens refers to equal voting rights, equal eligibility for public offices etc. In a sense, it is one man, one vote as per BR Ambedkar.
A democracy can exist without a written constitution. Britain is the best example.

Only 1 is correct.
Sovereignty simply implies that India is a state that takes its own decisions ultimately guided by the people.
No external agency dictates terms to India.
However, the notion of sovereignty does not seep into the framework of all democratic rights. For e.g. a sovereign state might very well discriminate between its citizens.
A sovereign state may very well restrict freedom of speech, as it is not an absolute right, even though it is vital to a democracy.

Statement 1 is incorrect.
• Article 1 describes India, that is, Bharat as a ‘Union of States’ rather than a ‘Federation of States’.
• According to Dr B R Ambedkar, the phrase ‘Union of States’ has been preferred to ‘Federation of States’ for two reasons: one, the Indian Federation is not the result of an agreement among the states like the American Federation; and two, the states have no right to secede from the federation.

All of the above are correct.
Values that inspired and guided the freedom struggle and were in turn nurtured by it, formed the foundation for India’s democracy. These values are embedded in the Preamble of the Indian Constitution. They guide all the articles of the Indian Constitution.
Taking inspiration from American model, most countries in the contemporary world have chosen to begin their constitutions with a preamble.
It contains the philosophy on which the entire Constitution has been built. It provides a standard to examine and evaluate any law and action of government, to find out whether it is good or bad. It is the soul of the Indian Constitution.

2 and 3 are incorrect.
Parliament shall have the power to make any provision with respect to the acquisition and termination of citizenship and all other matters relating to citizenship (Article 11).
The Government of India may waive all or any of the conditions for naturalisation in the case of a person who has rendered distinguished service to the science, philosophy, art, literature, world peace or human progress. Every naturalised citizen must take an oath of allegiance to the Constitution of India.
The Constitution (under Article 15) prohibits discrimination against any citizen on grounds of religion, race, caste, sex or place of birth and not on the ground of residence. This means that the state can provide special benefits or give preference to its residents in matters that do not come within the purview of the rights given by the Constitution to the Indian citizens. For example, a state may offer concession in fees for education to its residents.