Is it permissible to speak during the Tasbih of a thousand times on the night of Jumu'ah, and what is the ruling on that?

There is no authentic evidence specifying a thousand glorifications (tasbih) on the eve of Friday. However, there is no harm in glorifying a thousand times if it suits one's time and effort, and it is not obligatory to perform it continuously. It is better to glorify in a way that is most impactful and beneficial to the person, whether continuously or intermittently with rest periods. What is more important or achieves a greater benefit takes precedence over glorification, such as responding to a guest.