How sound are the mentioned hadiths that speak of cursing a place called "Tahwudah" and the Prophet, may God's prayers and peace be upon him, forbidding dwelling there? What is the ruling on dwelling in such cursed places? And have any hadiths been reported in the Sunnah that prohibit dwelling in cursed places?

The aforementioned Hadith (definition) in the question is fabricated and it is not permissible to attribute it to the Prophet, peace and blessings be upon him. Neither its chain of narration (sanad) is authentic, nor is its text (matn). It contains defects: the narration of Ishaq and his father is weak, Muqatil ibn Sulayman is a liar, and Wahb ibn Munabbih and Shahr ibn Hawshab are Tabi'un (followers, not Companions). Therefore, the reported narration is a mursal (missing the Companion in the chain) report and severely weak.

There is nothing in the authentic Sunnah (definition) indicating that the Prophet, peace and blessings be upon him, cursed a specific land or country and forbade residing in it, except what has been confirmed regarding the prohibition of entering the dwellings of those who wronged themselves. The place where a people who denied the truth were punished should not be inhabited or entered unless the visitor is weeping.