In this passage, the phrase "and she responded" can be considered an example of a signal phrase. A signal phrase is a phrase that leads into a quotation or statistic. These usually present the author's name, the reason for using the quote, or the context for the quotation. Signal phrases allow the reader to anticipate what he is about to read.
The actual name of the castle referenced in the play is Kronborg Castle, a real castle located on an area of land between Sweden and Denmark in Helsingor, which is the Danish name for Elsinore.
