As with so many of Shakespeare's speeches and lines that he gives to characters, I think it depends a lot on how a director of this excellent play wants to show these lines using subtext: what isn't in the play, but needs to be created to give it meaning. When we think of subtext, we think of non-verbal communication, emphasis, inflection and pauses, and by using all of these any actor can give their lines a variety of different meanings. It is one of the problems that we have, studying a play just from the page, rather than analysing it on the stage.
However, having said that, the first line, "Caesar, now be still," seems to reflect the acknowledgement of Brutus that Caesar is not lying still. Having been wrongfully killed, he hopes that his death will enable Caesar to lie still. The second line, "I killed not thee with half so good a will," could be paraprased as "I didn't kill you with the good intentions that I kill myself now." Again, this is a recognition that his killing of Caesar was not good, but that his own intentions for killing himself are better. I don't know if we can use these lines to state that Brutus is asking Caesar to forgive him. He does however clearly recognise that it was a bad thing to assassinate Caesar, and hopes that his own death will make amends somehow.