What are the acts of worship that are not valid without purity, and is it permissible for someone in a state of major ritual impurity (junub) or a menstruating woman to fast before ghusl, and is the recitation of the Qur'an accepted from one who is in a state of minor ritual impurity (muhdith)?

The acts of worship whose validity depends on purity from both minor and major ritual impurity are: Prayer, touching the Mushaf (the physical copy of the Qur'an), and circumambulating the Kaaba (Tawaf).

As for someone who is in a state of major ritual impurity, the following are added to these three: Remaining in the mosque and reciting the Qur'an. Purity is not a condition for fasting.