Can a spirit with dispelling dispel quickened spell from the astral plane?

A.

I don't think so. There's nothing in the text to indicate that quickened spells are any more astrally active than normal sustained spells.

Aren't spells by definition astrally active?

In 4th ed they explicitly state you must on the same plane the spell is on to dispell it. That would mean your spirit in the example could only dispell that spell from the astral if the spell was cast on the astral in the first place. 5th ed seems to be missing that distinction. Oversight or intentional, your guess is as good as mine.