What should the questioner do regarding the three days she vowed to fast due to losing her jacket, which she was unable to complete because of her illness, and what should she do with the money she found in her college that she was unable to return to its owner?

The fasting conditioned on the existence of the jacket is not obligatory to fulfill until it is found. As for the three days you did not condition, if the phrasing used was merely a promise and not an obligation (a vow), then they are not binding on you. If you obligated yourself to them and are unable to fast them due to an illness from which recovery is not expected soon, then the fasting is waived for you, and you are obligated to pay the expiation for an oath (kaffarat yameen), which is feeding ten poor people or clothing them or freeing a slave. Whoever cannot find that, then fasting three days. The money found is a lost item (luqatah); it should be announced for a year and is not a substitute for lost items. You must repent if you feel you have neglected religious duties.