Explanation:

Both the statements are correct. 

The election to constitute a Gram Panchayat shall be completed;
(a) before the expire of its duration specified in sub-section;
(b) in the case of dissolution, before the expiration of a period of six months from the date of its dissolution;
Provided that where the remainder of the period for which the dissolved Gram Panchayat would have continued is less than six months, it shall not be necessary to hold any election under this clause for constitution the Gram Panchayat for such period.

2nd statement is also correct. 

Every Panchayat elects a President or Sarpanch and a Vice-President or Upsarpanch. In some states the Sarpanch is directly elected by the Gram Sabha either through the show of hands or through secret ballot while in other states the mode of election is indirect.
He is an ex-officio member of the Panchayat Samiti and participates in its decision-making as well as in the election of the Pradhan and of the members of various Standing Committees. He acts as the executive head of the Panchayat, represents it in the Panchayat Samiti as its spokesman and coordinates its activities and those of other local institutions like cooperatives.