Are the hadith that state: Al-Hasan said, (Whoever performs ablution and prays four rak’ahs, and recites this supplication, his prayer will be answered, whether he is in distress or not in distress), authentic? And the supplication is: "Ya Wadud, Ya Wadud"?

There is no authentic Hadith from the Prophet, peace and blessings be upon him, that specifies a particular supplication that will be answered for someone who performs ablution, prays four rak'ahs, and then recites it, whether in distress or not. The mentioned story about Abu Mu'allaq Al-Ansari and his supplication, "O Most Loving, O Lord of the Glorious Throne...", is one of the miracles of the awliya' (saints) and not a prophetic Hadith.

Authentic prophetic supplications for distress and worry:

Ibn Mas'ud's supplication: "O Allah, I am Your servant, son of Your servant..." Nufay' ibn Al-Harith's supplication: "O Allah, I hope for Your mercy, so do not leave me to myself even for the blink of an eye..." Ibn Abbas's supplication during distress: "There is no god but Allah, the Almighty, the Forbearing..." Asma bint Umays's supplication: "Allah, Allah, my Lord, I do not associate anything with Him." Dhul-Nun's supplication: "There is no god but You; glory be to You! Indeed, I was among the wrongdoers."