What is the ruling for someone who finished Fajr prayer two minutes after sunrise, knowing that he cannot maintain his ablution? And what should he have done if the same thing happened to him with Maghrib prayer?

If the delay in prayer is due to a legitimate excuse, such as sleep, then there is no blame upon you. However, you are sinful if the delay is without an excuse.

You will be rewarded if you delay prayer for the purpose of proper purification (ṭahārah), but it is not permissible to delay it until its time expires except for combining prayers. For instance, one afflicted with flatulence may combine two prayers with a valid ablution. The time for Fajr prayer expires at sunrise, and whoever catches one rakʿah before sunrise has caught the prayer.

If a person afflicted with flatulence finds a time that suffices for performing the prayer with proper purification, then it is obligatory for him to do so. If he does not find such a time, he should perform ablution for each prayer and pray, and what exits from him during the prayer will not harm him, nor is he required to repeat it.