Does the Imam's saying to the worshippers "Unify God" or "Send blessings upon the Prophet" during the Friday sermon count as a frivolous act that invalidates the Jumu'ah (Friday prayer), and is it obligatory for the worshippers to comply with that?

Idle talk during the Friday sermon does not invalidate it, but it diminishes its reward. It is preferable for the preacher not to command the worshippers to send blessings upon the Prophet or to declare the Oneness of Allah, as there is no authentic narration from the Prophet (peace be upon him) supporting this. Indeed, he would command and prohibit in his sermon when there was a compelling reason to do so.