A: She has immense spiritual power, maybe that could be the reason.
A: She was known as the "special person" that mentioned by Kaede and Kikyo (in anime or manga).
A: Kagome is a priestess that possesses the power of purification. Miroku, who may be a monk and possesses spiritual powers, does not possess the same ability. Kagome's spiritual powers of purification due to her pure heart and kindness makes her purify the miasma. It's probably similar to how she can purify jewel shards at a single touch and often uses her arrows of purification to get rid of large amounts of miasma to protect her friends.