The fundamental point to understand is that those names aren't spelled the same, they're written the same. The writings and readings are essentially distinct things; neither is a representation of the other.
(As an aside, Japanese doesn't really have spelling as we think of it. It has phonetic characters, but their names map 1:1 with their pronunciation, so "spelling" a Japanese word is the same thing as just saying it.)
Not quite, eg ki'yu vs kyu vs ki'u and n'a (んあ) vs na (な), but unlike in english those tend to be pathological corner cases that you can either ignore entirely in practice or easily handle (eg the Ci+yV <-> CyV convention).
k-ee-y-oo and k-y-oo are distinct pronunciations that are both written as kiyu (きゅ) (also not 1:1, though this could be considered a accent maybe?)
I wasn't trying to make a point, beyond "spelling a [any] word is not just the same thing as saying it".
きゆ and きゅ are pronounced differently because they're spelled differently (notice the size of the ゆ). Same goes for んあ and な.
That is, you say the word たに by saying た and then に, and you say the word たんい by saying たん and then い. Equivalently if you were to "spell" the word きゅう you'd say きゅ and then う -- you wouldn't say き・ゆ・う because that would be a different word.
(Incidentally na and n'a are not pronounced the same, as the previous example hopefully illustrates.)
I'm also not sure what you mean by kiyu and kyu, since きゆ and きゅ are clearly orthographically distinct.
Ki-yu (きゆ) and Kyu (きゅ) arr distinguised by the size of the ゆ character