The answer of the ninth riddle - She Who Was Forgotten
The first line "Introduced in the first early era"
» The first season of DC.
The second line "On a case of attempt murders"
» At least two attempt murders occurred on 'the case'.
The third line "And the axe-holding black cape man."
» Seemed to be the culprit...someone who was holding an ax and was wearing a black cape.
The fourth line "Then she had appeared three more times"
» 'She' must had made an appearance on 'the case' and she had been appeared again for 3 times. (and yes, as RainbowKittyRune pointed out, it will be two if you counted two-episodes case as one episode.)
- The fifth line "Before never presented or even mentioned again"
» She was never mentioned again after that. Look like a throwaway character (So sad T.T)
The sixth line "Though her sibling still often on the scene"
» She had one sibling, who seem to be one of 'often-presented' characters.
The seventh line "As one of the cases-bringers"
» Wherever her sibling go, there's a case, like Conan.
The eighth line "And sorta became certain thief's instigator"
» 'Certain thief' was Kaito Kid (Who wouldn't knew that?), meant her sibling was also appeared on his heist (and was his fan).
The ninth line "Cheerful and confident"
» Her sibling was very cheerful and had a lot of confidence.
The tenth line "Unlike her gentle and kind"
» Opposite to her, as she was very gentle, and kind.
The eleventh line "So who and how old was she?"
» This was the question...
So...
She was introduced in the first season, on the case where there's a lot of attempt murders happened. The culprit had an ax and wore black cape. She then appeared again for 3(or 2) times and was very well disappeared from the face of the earth.
She had a sibling who brings case and being the Kid fan, who had quite opposite personality to her.
The riddle asked who she was and how old she was.
Haibara was instantly crossed out, she wasn't apparently gentle like 'she' did.
Akemi was out too, because she wasn't a case bringer(not Kid fan either), and she appeared (or at least mentioned on the background.) more than three times.
Sera Masumi was also out, as she wasn't introduced in the first season.
Tsuburaya Asami (Mitsuhiko's elder sister.) outed, she was never presented at the case's scene, and we didn't know much about her.
Who's missing?
Suzuki Ayako! She was a character too, you know? As Sonoko's elder sister. She's also first appeared on the first season, on the 'Bandage Man case' (Ep.34-35). She was very kind and polite person unlike her sister. But she was only the minor character, I'm a little sad knowing that T.T
Seem like I'm getting lazier...Oh well, no one read it anyway. So let's just move on...