What should I do with money that is owed to me by a deceased non-Muslim teacher whose family I cannot find, and the cost of one month in a Qur'an memorization center that has closed down, and transportation fees paid to me by someone I do not know?

You must strive to deliver the funds to their owners or their heirs. If, after searching, it is impossible to deliver them, then spend them on public welfare and charitable causes.

As for the Quran memorization center, closing it does not exempt you from returning the month's fee to those who were running it, unless you despair of reaching them. In that case, the amount should be spent on charitable causes.