the thing that "she has the ability to sing in the alto range to coloratura soprano range that's why she's classified as lyric-coloratura soprano" is illogical. a soprano can't reach the alto range, that would be a contralto not a soprano.
what do you mean "her voice is also rumored to reach 4th to 5th octave by just using her chest voice"? 4th octave is reached by chest voice of course and the 5th octave too except A5 and B5 which can be reached by head voice/falsetto.