Does the saying "Every step is an expiation for an oath" mean repeating the expiation according to the number of steps, or is it an estimation of the number of expiations? And are thousands of expiations required based on the saying of Imam Malik regarding someone who vowed, "I owe ten expiations"?

The vow in question is a vow of 'lajaj' (obstinacy or contention), which necessitates one of two options: either offering expiation for each step, or a single expiation for an oath (kaffarat yamin) which nullifies the obligation of the vow. This is the view of the majority of scholars. However, Imam Malik holds the view that fulfilling the vow of 'lajaj' is obligatory, meaning expiating for each step. The preponderant view is that of the majority of scholars. Ibn Qudamah stated in "Al-Mughni" that the ruling for a vow of 'lajaj' or anger is that one is given the choice between fulfilling what was sworn upon or breaking the oath and offering expiation for an oath (kaffarat yamin). He supported this with the sayings of Umar, Ibn Abbas, and other Companions, and with the Hadith: "There is no vow in anger, and its expiation is the expiation of an oath." And with the Hadith of Aisha that the Prophet, peace and blessings be upon him, said: "Whoever swore to walk, or offer a sacrifice... its expiation is the expiation of an oath." And due to the generality of the verse: {But He will call you to account for what your oaths have intentionally bound you to; then its expiation is the feeding of ten poor people.} [Al-Ma'idah 5:89]. The vow of 'lajaj' resembles an oath from one aspect and a vow from another, so one is given the choice between fulfillment and expiation.