Is Cassius Caesar's friend?
No, Cassius is not Caesar's friend. Their relationship is nothing like the relationship between Brutus and Caesar. Note what Cassius says about Caesar in his soliloquy at the very end of Act 1, Scene 2.
Caesar doth bear me hard, but he loves Brutus.
My edition of Julius Caesar footnotes "bear me hard" as "bear a grudge against me."
Caesar expresses a very negative opinion of Cassius while talking to Antony in Act 1, Scene 2.
Yon Cassius has a lean and hungry look.
He thinks too much. Such men are dangerous.
And a little later
Such men as he be never at heart's ease
Whiles they behold a greater than themselves,
And therefore are they very dangerous.
Cassius may have a personal reason for wanting Caesar assassinated. He may be afraid that if Caesar attained absolute power he would purge a number of Romans including himself. Cassius is a very selfish person who cares much less about the good of Rome than about the good of Cassius.
So Cassius and Caesar are both afraid of each other. They are not friends.
Gaius Cassius Longinus was a historical figure who would have been well known to Shakespeare's audience from such authors as Plutarch, Suetonius, and Cicero, all of whom would have been standard fare in English schools of the period. Cassius was a member of a faction known as the Optimates, who were strongly opposed to Julius Caesar, the leader of the opposing faction of the Populares.
Cassius had sided with Pompey in his conflict with Caesar and even commanded one of Pompey's fleets. Although by the time in which Shakespeare's play is set, there was a temporary truce between these factions, that truce simply meant a temporary cessation of outright war rather than a move toward friendship or reconciliation. Thus Caesar's suspicions of Cassius were grounded in their past history.
The two had always been on opposite sides politically, and Cassius was especially ambitious and jealous; he believed that Caesar was limiting his potential for political advancement. Cassius and Caesar were not friends.