In this scene, the soothsayer is warning Caesar about the Ides of March. The Soothsayer says to Caesar "Beware the Ides of March" (I:ii:ln 18). I believe that this scene is important because the Soothsayer is warning Caesar about any potential harm that not being aware could put him in. The Ides or March is a "bad" luck day.
Act IV: Scene iii
The conspirators visit Brutus because they want him on their side. The conspirators say "Give me your hands all over, one by one" (II:i:ln 112). Brutus decides to join the conspirators because he compares Caesar to a serpent's egg. Once he hatches, it's bad, but until then, it'll be okay.
Act V: Scene V
This is when the conspirators approach Caesar to kill him. "Et tu Brute? Then fall Caesar" (IIl: i: ln 79). They are killing Caesar because he's like a serpents egg. He's not dangerous until hatched, but once hatched, he is dangerous. The conspirators stab Caesar 23 until he finally falls to the floor and dies.
Be careful who you trust
Brutus was in his tent reading, getting ready for the battle at Phillipi. Brutus saw a ghost, which was the ghost of Caesar. Brutus asked the ghost what he was doing, and the ghost says "To tell thee thou shalt see me at Phillipi" (IV:iii:ln 282).
At the beginning of this scene, Brutus is planning on killing himself. He asks one of his men if he will hide his face while holding the sword. As the men is doing so, Brutus throws himself onto the sword. The conspirators come in and say "Now be still, I killed not thee with half so a good will" (V:V: ln 50-51).
Brutus had a lot of trustworthy people in his life. Brutus says that he has not found one man that he couldn't trust. "I found no man but he was true to me" (V:V: ln 35). Brutus then continued on to kill himself. Brutus had a very successful life, and clearly was very careful on who he chose trust.