Accurate Claims about what Happens in Titus Andronicus, the play?

Is it true that Titus' sons help him capture Chiron and Demetrius?
Is it true that Titus raises an army of Goths?
Is it true that Titus is too old to be emperor and therefore he tells his son, Lucius, to raise an army of Goths so he  himself, Titus, can continue his revenge on Tamora?
Is it true that Titus kills Tamora by stabbing her in the neck?
Does Titus have a friend named Lucius?