Explanation:

First statement is incorrect.Collegiums system in India is the system by which the judges are appointed by the judges only also referred to as “Judges- selecting- Judges”. The removal of judges is through Parliament and not by collegium.
It is the system of appointment and transfer of judges that has evolved through judgments of the Supreme Court, and not by an Act of Parliament or by a provision of the Constitution.
The Supreme Court collegium is headed by the Chief Justice of India and comprises four other senior-most judges of the court. A High Court collegium is led by its Chief Justice and four other senior-most judges of that court.
Names recommended for appointment by a High Court collegium reaches the government only after approval by the CJI and the Supreme Court collegium.

Second statement is correct Under the collegium system, the executive has no say in judicial appointments. The recommendations of the collegium of judges are final and binding on the government.

Third statement is correct In 2017 in the interest of transparency, accountability and a more robust legal system, the Supreme Court Collegium comprising of top five judges has agreed to put the reasons for the appointment and rejection of judges online. To begin with this practice, the SC has posted online reasons for its recommendations for judicial appointments to the Madras HC and the Kerala HC

Fourth statement is also correct In 2015 the Constitution Bench of the Supreme Court declared National Judicial Commission (NJAC) as Unconstitutional because it violates Basic Structure of Constitution of India.

There is no mention of the collegium either in the original Constitution of India or in successive amendments.