Is "قدرُ الله" (with a dammah on the ra) a correct reading of the Prophetic Hadith, and what is the difference in meaning between it and the reading "قدرَ الله" (with a fatha on the ra)?

Both forms are correct and convey the same meaning. Al-qadar (definition) (قدر) is a verbal noun derived from qaddara al-shayʾ (قدر الشيء), and its infinitive is al-taqdeer (التقدير). If you read qadar Allah (قدر الله) with a rafʿ (nominative case) on the qaf, taking it as a noun, then it is the predicate of an omitted subject, the تقدير (estimation) of which is "هذا قدر الله" (This is Allah's decree). If you read it with a shaddah on the dal and a fatḥah on the rāʾ, it is a past tense verb.