According to wiktionary, "mwuguzi" and "muuguzi" are alternate forms https://en.wiktionary.org/wiki/muuguzi#Swahili https://en.wiktionary.org/wiki/mwuguzi#Swahili (the plural should be "wauguzi"; no alternatives and Swahili doesn't contrast definite and indefinite articles in it's words)
Don't know but "mwuguzi" is not included in the dictionary hints. I don't find it in my regular Swahili dictionary. Only "muuguzi." I think it is a typo.
As clh335763 says, the English Wiktionary states that mwuguzi is an alternate form of muuguzi.
No, those would be the same regardless of which spelling you choose. The are just alternative spellings.
Hmmm, it is telling me that both Mwugzi and Muuguzi are wrong and the correct word is now Nesi?!