Did Brutus love Caesar

No, he was not. Nor was he acting for the Republic.

If a man truly believes that he must kill for an ideal, than he does so. On the other hand, if he is cowardly and simply wishing to follow the crowd, then one might see him wait till others have done the killing, then step in at the end so as to not be left out.

History has recorded that Brutus only stabbed when the deed was already done, and Caesar lay bleeding and helpless. This is why his name - like the name of Judas - is known, but not used.