Am I sinful for breaking the oath in which I swore to refrain from eating before prayer, and am I sinful every time I eat before prayer?

What you did by breaking your oath is not sinful, and it may even be preferable if it leads to a benefit; this is based on the saying of the Prophet, peace and blessings be upon him: "Whoever swears an oath, then sees something else as better than it, let him expiate for his oath and do what is better." This breaking of the oath necessitates an expiation for the oath, and your oath is dissolved by it, so you are not required to offer another expiation if you repeatedly eat before prayer. The expiation may be repeated in specific cases, such as when you intend for the expiation to be repeated with the repetition of eating, or if the wording of your oath implies repetition, such as saying: "Every time, or whenever I eat before prayer, an expiation for an oath is due upon me."