What is the ruling on someone who swore in writing upon himself to recite a section of the Qur’an, pray two rak'ahs, and give charity for every congregational prayer he misses, then did not fulfill it? Is a single expiation for an oath incumbent upon him, or an expiation for each prayer he missed?

An oath is not established by writing unless there is an intention. If you did not intend to make an oath by what you wrote, then there is nothing binding upon you if you did not read a part (of the Quran) and did not pray two rak'ahs due to missing the congregational prayer.

However, if you did intend to make an oath, then if you miss the congregational prayer and do not pray two rak'ahs and read a part, you have two options: either to break the oath by not giving charity and thus pay an expiation for the oath, or to give charity with money. This ruling applies to every prayer you miss in congregation if you intended it, because an oath is based on the intention of the swearer.

And if you do not remember the amount of money to be given in charity, then if you intended a specific amount, give it. Otherwise, giving charity with money that has value, whether little or much, will suffice you.