Does the expulsion of phlegm or the sound of saliva from the mouth invalidate the recitation during prayer, and what is the ruling on the prayer of one whose voice trembles when extending the word "walad-dalleen" in Surat Al-Fatiha?

Prayer is not invalidated by the expulsion of phlegm or the movement of saliva, as these are involuntary actions. As for the voice trembling when extending "wa la ad-dalleen," there is no mention of this among the jurists. However, the important thing is to pronounce all the letters of Al-Fatihah with their proper intensifications (tashdeed). If one intensifies a letter that is supposed to be light, it is acceptable, as is repeating a letter unintentionally. One must also be careful of waswasah (whispers of Satan/obsessive doubts).