F3 is part of a whole idea of how to develop your pieces and attack. Qd2, 0-0-0, g4, h4 and h5 is the start of a ferocious attack against black's castled king. This is called the Yugoslav attack against the Dragon variation of the Sicilian defense and its very strong. https://www.365chess.com/opening.php?m=13&n=1135&ms=e4.c5.Nf3.d6.d4.cxd4.Nxd4.g6.Nc3.Bg7.Be3.Nf6&ns=3.3.4.4.3.3.4.7427.7439.23890.19654.1135
To the extent you are asking about other natural looking moves like bc4 or be2, the question is a bit too broad for me to address in the air. Also, candidly, a master might be able to give a better explanation as to those issues.
Engine shows f3 should be played by white. what is the purpose of playing f3 now?