With reference to Deputy Speaker of Lok Sabha, consider the following statements:

1 As per the Rules of Procedure and Conduct of Business in Lok Sabha, the election of Deputy Speaker shall be held on such date as the Speaker may fix.
2. There is a mandatory provision that the election of a candidate as Deputy Speaker of Lok Sabha shall be from either the principal opposition party or the ruling party.
3. The Deputy Speaker has the same power as of the Speaker when presiding over the sitting of the House and no appeal lies against his rulings.
4. The well established parliamentary practice regarding the appointment of Deputy Speaker is that the motion is moved by the Speaker and duly seconded by the Prime Minister.

Which of the statements given above are correct?

The correct answer is 1 and 3 only.

Let us analyze each of the statements step-by-step to understand why they are correct or incorrect:
Statement 1 is correct: According to Rule 8 of the Rules of Procedure and Conduct of Business in Lok Sabha, the election of the Deputy Speaker is held on a date that the Speaker of the Lok Sabha may fix. The Speaker will then instruct the Secretary-General to send a notice of the date to every member.
Statement 2 is incorrect: There is no "mandatory provision" (constitutional or statutory) that the Deputy Speaker must be elected from either the principal opposition party or the ruling party. Up to the 10th Lok Sabha, both the Speaker and the Deputy Speaker usually belonged to the ruling party. Since the 11th Lok Sabha, there has been a consensus (an informal parliamentary convention, not a mandatory provision) that the Speaker comes from the ruling party (or ruling alliance) and the post of Deputy Speaker goes to the main opposition party.
Statement 3 is correct: The Deputy Speaker performs the duties of the Speaker's office when it is vacant or when the Speaker is absent from a sitting of the House. In both cases, the Deputy Speaker enjoys all the powers of the Speaker, including presiding over joint sittings of both Houses. No appeal lies to the Speaker against any ruling given by the Deputy Speaker when presiding.
Statement 4 is incorrect: According to the established parliamentary procedures, at any time before noon on the day preceding the date fixed for the election, any member may give notice of a motion that another member be chosen as the Deputy Speaker. This motion is moved by a member of the House and seconded by another member, rather than being formally moved by the Speaker and seconded by the Prime Minister.

Therefore, only statements 1 and 3 are correct.