Is Cassius in Julius Caesar a round, flat, static or dynamic character?
I don't think Shakespeare really writes flat or static characters: it seems to me that there is always both a sense of character development (and that what we know about a character goes forward in the play) as well as a sense of complexity (i.e. that it's difficult to reduce the characters to stock 'types' or stereotypes).
Cassius supports my thesis. For a long time, people basically agreed with Caesar's assessment of him:
Yond Cassius has a lean and hungry look;
He thinks too much: such men are dangerous.
He is dangerous indeed. He knows exactly how to persuade the arrogant Brutus into the conspiracy, comparing Brutus' name to Caesar's and asking why Caesar is so much more powerful than Brutus:
Brutus and Caesar: what should be in that 'Caesar'?
Why should that name be sounded more than yours?
He is indeed a shrewd contriver who knows exactly how to persuade people. He has no wife as far as we know in Shakespeare's play (unlike both Brutus and Caesar) though he does seem extremely personally attached to Brutus, despite his wililngness to persuade and manipulate him.
On the one hand he's bitter and ambitious:
Why, man, he doth bestride the narrow world
Like a Colossus, and we petty men
Walk under his huge legs and peep about
To find ourselves dishonourable graves.
Yet he's not just the 'baddie'. Every tactical decision he suggests in the play - killing Antony as well as Caesar, his battle plan, his insistence that Antony should not be allowed to speak at Caesar's funeral - is right. And yet Brutus never listens to him. He's the best tactician - and possibly the brightest character - in the play. Yet he never gets his own way.
And, even though he dotes on Brutus (read that argument in the tent from Act 4) at the end of the play, who does he say this line about?
O, coward that I am, to live so long,
To see my best friend ta'en before my face!
Not Brutus. But Titinius. What do you make of that?
Cassius indeed is a complex and rounded character.
Dynamic - recall how he moves and persuades Brutus to join the conspiracy "i am glad that my weak words have struck but thus much show of fire in Brutus"
Weak words indeed - Cassius uses powerful words combined with imagery to persuade others....but eventually his threats don't affect Brutus...but the evil had already been done. Therefore, Cassius is very much dynamic in every way