parshanut torah comment - Did Moshe need to do all 3 signs for the Jewish people and if so why?

In Shemos 4:1 Moshe expresses his concern to God that the people will not believe that he was commanded by God to take them out. God then gives him 3 signs (4:2-9) stating that if they won't believe [that Moshe was sent by God as a result of] the first sign they will believe the later (2nd) and if they don't believe as a result of either of those they will do so as a result of the 3rd sign.

Later on (4:30) he (Aron? Moshe?) performs the signs and (4:31) the people believed. My questions are

1. Did the need to perform only 2 of the signs or all 3


2. If the needed to perform all 3 why were the first 2 not enough


3. I recall learning (I believe in Gemarah Sotah) that the Jews were instructed not to believe any would-be savior until he spoke the words 'Pakod Yifkod' and that when Moshe came and performed the signs the people went to Serach bas Asher and told her, she said to ignore it. But when they told her he used the phrase 'Pakod Yifkod' she said to believe. - If so what was the point of the signs at all?