How does Livia die and at which point in the novel does she use the emperor's envelope seal to send false letters of execution?
When the emperor Augustus was alive, Livia, his wife, had tremendous power and influence, and she had access to his seal, which was almost like his signature. For instance, when Livia wanted to know what changes Augustus had made to his will, she convinced the head Vestal to let her see it because she could seal it back without anyone's ever knowing she had read it.
As to your question about how she used the seal to send false letters, Livia wrote a letter in Tiberius's name to make it appear that Piso and Plancina could not have been guilty of killing Postumous. She had had power over Augustus, and she thought she could do the same with Tiberius. Her intention was to absolve the couple of their guilt, but her plan backfired. Tiberius refused to acknowledge the letter as his own and planned to announce that it was a forgery at Piso's trial. Plancina, however, was persuaded to clear herself and Livia by killing Piso.
Livia died of old age, after having confessed to Claudius about all the murders she committed.