What manner of belief? The demons believe and tremble, but they are not saved. The key is in here:
Romans 10, NASB
8 But what does it say ? "THE WORD IS NEAR YOU, in your mouth and in your heart " - that is, the word of faith which we are preaching,
9 that if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved;
10 for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation.
This is part of #1, the repentance being an agreement with God that we are indeed sinners in need of a savior, and He is Christ.
Absolutely
unnecessary for salvation. It is but an outward testimony of the inward workings of the Holy Spirit to bring about faith of a salvic nature.
Which happens the instant you have believed to the point of salvation.