Does repeating a part of an ayah from Surat Al-Fatihah by the Imam invalidate the prayer, such as when he says: "You have bestowed favor upon them, not of those who have evoked [Your] wrath," then repeats: "You have bestowed favor upon them, not of those who have evoked [Your] wrath or of those who are astray"?

The Imam should know where to pause and where to resume recitation (waqf and ibtida'), as this involves perfecting the pronunciation of letters and understanding the correct places to stop. Stopping in an inappropriate place or resuming at an incorrect point might change the meaning of the verse. If he stops incorrectly, he should re-start from a point where it is permissible to resume, so that the meaning is sound. What the Imam did does not invalidate his prayer or the prayer of those behind him.