Only statement 1 is correct.

• The Preamble has been amended only once so far, in 1976, by the 42nd Constitutional Amendment Act, which has added three new words—Socialist, Secular and Integrity—to the Preamble.
• It is part of Indian Constitution. Constitution derives its authority from the People of India.

Both statements are correct.

This is a provision given under Article 16 (4) of the Constitution.
Article 16 provides for equality of opportunity for all citizens in matters relating to employment or appointment to any office under the State. It prohibits discrimination on grounds other than those mentioned in the article itself.
The NCBC Act, 1993 established the National Commission for Backward Classes. The commission was the outcome of the direction of the Supreme Court in the Mandal case judgement.

In the Menaka case (1978), the Supreme Court overruled its judgement in the Gopalan case by taking a wider interpretation of the Article 21. Therefore, it ruled that the right to life and personal liberty of a person can be deprived by a law provided the procedure prescribed by that law is reasonable, fair and just.
In other words, it has introduced the American expression ‘due process of law’. In effect, the protection under Article 21 should be available not only against arbitrary executive action but also against arbitrary legislative action.
Further, the court held that the ‘right to life’ as embodied in Article 21 is not merely confined to animal existence or survival but it includes within its ambit the right to live with human dignity and all those aspects of life which go to make a man’s life meaningful, complete and worth living. It also ruled that the expression ‘Personal Liberty’ in Article 21 is of the widest amplitude and it covers a variety of rights that go to constitute the personal liberties of a man.

1, 4 and 5 are correct.

Preamble: The words “JUSTICE, social, economic and political; EQUALITY of status and of opportunity; and to promote among them all FRATERNITY assuring the dignity of the individual and the unity and integrity of the Nation”.
First Schedule: It talks about Indian states and Indian territory.
Third Schedule: It contains forms of Oaths and affirmations for office holders.
Fundamental Rights:
IA 23. Prohibition of traffic in human beings and forced labour
A 24. Prohibition of employment of children in factories, etc.
Directive Principles of State Policy:
A38. State to secure a social order for the promotion of welfare of the people

A39 (only first part) – The State shall, in particular, direct its policy towards securing – (a) that the citizens, men and women equally, have the right to an adequate means of livelihood