Is it permissible to purchase the item sworn upon now, and cease observing the fasting for the expiation of the oath, knowing that the intention was to purchase it shortly, and several days have passed?

If you specified a time to purchase something and swore an oath regarding it, then the time passed and you did not buy it, you are obligated to offer expiation (kaffarah (definition)) even if you purchase it later. This is because the oath is based on the intention of the one who swore it, and expiation becomes obligatory upon breaking it. The expiation for an oath is to feed ten poor persons, or to clothe them, or to free a slave. If one cannot find [any of these], then it is to fast for three days, and continuity is not a condition for fasting them.