“give these bills”
'Bills' here means written military orders or dispatches, not money. Brutus is sending Messala to deliver written commands to the legions positioned on the far side of the battlefield.
- TLN 2346historical topical
“cold demeanor in Octavius' wing”
'Cold demeanor' means sluggish, unenthusiastic fighting behavior. Brutus has spotted that Octavius's flank of the enemy army seems reluctant or hesitant, and he means to exploit that weakness before it stiffens.
classical Plutarch's Lives (North's Translation) “sudden push gives them the overthrow”
'Overthrow' means total defeat or rout, and 'push' means a sharp, concentrated assault. Brutus is saying that a swift, unexpected charge right now, while Octavius's men are hesitating, will break them completely.