Are my previous prayers valid, considering I used to utter the intention in my heart, and is it permissible to feed ten poor people inexpensive food if I don't possess the full amount for the expiation of an oath?

Uttering the intention for prayer is not forbidden. Some scholars consider it legislated, while others deem it an innovation due to lack of evidence. It is permissible according to the Maliki school, meaning it is contrary to what is superior (khilaf (definition) al-awla), and it is better not to utter it because the place of intention is the heart. As for the Hanafi and Shafi'i schools, and one narration from the Hanbalis, they recommend uttering it. In any case, uttering it does not affect the validity of the prayer.

The expiation for an oath (kaffarat al-yamin (definition)) is feeding ten poor people, or clothing them, or freeing a slave. If one is unable to do any of these, then fasting for three days. The feeding must be from the average food consumed by one's family; it is not required to be the best, nor is the lowest sufficient. Therefore, buying cheap food for expiation is not sufficient; rather, one must feed ten poor people from the average food of one's household.