Is preparing breakfast and overseeing household matters considered like someone who breaks a fast? And is the doer of good rewarded for her household chores if she intends them for the sake of Allah?

The reward for preparing food for fasting people is the same as the reward for feeding them, because the one who manages something receives a reward similar to the doer. All the actions you undertake will be rewarded as long as you do them seeking Allah's pleasure. However, it is not permissible to delay the prayer beyond its prescribed time, for "Indeed, prayer has been decreed upon the believers a time-constrained ordinance." Good deeds are nullified by neglecting it, and delaying it beyond its designated time is a form of neglect. You must hasten to repent. As for delaying the prayer from the very beginning of its time, there is no harm in that, but you miss the virtue of praying at the earliest time.