Are Mulazim ibn Amr al-Yamami and al-Hanafi the same person? And is Abdullah ibn Badr the father of Mulazim ibn Amr, from whom he narrated?

Mulazim ibn Amr ibn Abdillah ibn Badr Al-Hanafi Al-Yamami is trustworthy. He was declared trustworthy by Al-Bukhari, Ibn Abi Hatim, Al-Ijli, Ibn Ma'in, Al-Nasa'i, and Abu Zur'ah. As for Abdullah ibn Badr, he is his grandfather, and he was declared trustworthy by Yahya ibn Ma'in and Abu Zur'ah.