What is the authenticity of the narrations concerning specific prayers and supplications for fulfilling needs, and is it permissible to act upon them?

The four forms mentioned for the Salah of Need (Salat al-Hajah) are not all legislatively established; only the first form is. The latter three forms have not been proven by any legal evidence. Al-Shawkani weakened all the wordings and forms of the Salah of Need except for the hadith of Abu al-Darda and the hadith of Ibn Abi Awfa. The hadith of Abu al-Darda was narrated by Imam Ahmad, and Shu'ayb al-Arna'ut deemed its chain of narration weak. Therefore, one must limit oneself to the first form and abandon all others, because good lies in following the guidance of the Prophet, peace and blessings be upon him, and evil lies in innovating in religion.