Is the prayer of one who is able to recite Al-Fatihah with tajwid valid if he does not do so? And what is the opinion of the four madhhabs on this?

The prayer is valid without tajwid (recitational rules) of Al-Fatiha for someone capable of tajwid, as long as they pronounce the letters from their correct articulation points and observe the vowelizations; because anything beyond that in tajwid is supererogatory and not obligatory. The obligatory tajwid is that which safeguards against clear grammatical errors (lahn jali) that alter the meaning. As for subtle grammatical errors (lahn khafi), they do not invalidate the recitation. Ibn 'Uthaymin and Ibn Baz mentioned that tajwid is for beautifying the voice and is not obligatory, and what is important is the correct pronunciation of the letters.