Explanation:

First statement is correct.
All the seats in a Panchayat shall be filled by persons chosen by direct election from territorial constituencies in the Panchayat area and; for this purpose, each Panchayat area shall be divided into territorial constituencies in such manner that the ratio between the population of each constituency and the number of seats allotted to it shall, so far as practicable, be the same throughout the Panchayat area.
Second statement is incorrect.
Gram Sabha means a body consisting of all persons whose names are included in the electoral rolls for the Panchayat at the village level.
Third statement is incorrect. Within the Constitutional framework, ‘Panchayats’ is a State subject. Under Article 243G, State legislatures may endow Panchayats with powers and authority to enable them to function as institutions of self-government and plan and implement schemes for economic development and social justice including on matters listed in the Eleventh Schedule.
Fourth statement is correct. Directive Principles of State Policy lays down that the State shall take steps to organise village panchayats and endow them with such powers and authority as may be necessary to enable them to function as units of self-government. As per the constitution the states devolve powers and functions to the Panchayats to enable them to function as tools of local self government.