What are the type of "haa'" and the madd in "هذه جهنم" (this is Hell) and "هذه أمتكم" (this is your nation), and are they a "haa'" of a pronoun or do they have a special ruling due to their difference from the masculine pronoun?

The "ha" in "hadhihi" is not a possessive "ha" (ضمير), but rather a "ha" of a demonstrative pronoun for the feminine. However, it has been treated like the possessive "ha" in its rulings. Therefore, the "ha" in "hadhihi Jahannamu" (this is Hell) is subject to the minor prolongation (silah sughra) and is extended with a natural prolongation (madd tabi'i). Whereas the "ha" in "hadhihi ummatukum" (this is your nation) is subject to the major prolongation (silah kubra) and its extension is treated like the disconnected prolongation (madd munfasil), being shortened, moderately prolonged, or fully prolonged depending on the recitation (riwayah).