Is it permissible to connect and pause while reciting Al-Fatihah, such that the worshiper pauses after "All praise is due to Allah, Lord of the worlds," and then continues with "Lord of the worlds, The Most Gracious, the Most Merciful"? And is this considered an innovation (bid'ah)?

There is no harm for the Imam in stopping and resuming as described, and his action is not an innovation, even if it deviates from the continuous Sunnah in recitation. Indeed, Imam Ibn Al-Jazari explicitly stated the permissibility of pausing at the end of verses, as it was reported from the Prophet (peace be upon him) in the hadith of Umm Salamah (may Allah be pleased with her) that the Prophet (peace be upon him) used to recite by pausing at the end of each verse. Moreover, some scholars considered pausing at the end of verses a Sunnah, and it is preferred by Abu Amr and Al-Bayhaqi and others, who said that it is better to pause at them, even if they are connected to what follows them, because following the guidance and Sunnah of the Messenger (peace be upon him) is more paramount.