My reading of this character is that Brutus' philosophical interests are real only in the description of his character, only superficially, and are not really enacted in the play.
Brutus stoicism does not seem to enter into his debates with Cassius nor into his decisions.
Yes and no. Brutus is able to block his grief for Portia, who has killed herself at home by consumming hot coals, but his ignoring of his feelings regarding Cassius seem to effect his demise rather than assist him as he egotistically feels his stoicism makes him stronger and a better judge of situations.
The simple answer to this question would be "yes." Stoicism was prized partly because it was considered a way of controlling the emotions by using reason. (In this respect, it very much resembles contemporary "cognitive psychology"). Of course, one might argue that if Brutus were a true stoic, he would not have become involved in the killing of Caesar, although the counter-argument is that he sees the killing as his patriotic duty to Rome.