Does the first heart sound occurs at the same time as the P wave of the ECG?

Answer 1

No. The p wave indicates initial depolarization of the conduction fibers, and is FOLLOWED by actual cardiac muscle contraction (miliseconds later).

Answer 2

No, it occurs just after it. The heart sounds are of the valves closing and the P-wave is the atriums firing. It is after it fires and the bicuspid and tricuspids valves close that you hear the sound. The second sound you hear is the pulmonic and aortic valves closing and that happens right after the QRS wave.