What is the ruling regarding the Maghrib and 'Isha prayers that were not performed due to the onset of water discharge before childbirth, and what is the ruling regarding the Fajr prayer performed with an ablution that preceded an internal examination, after which the ablution was not renewed?

The discharge you saw before childbirth does not prevent prayer. You were obligated to perform ablution (wudu') and pray when the discharge stopped. If it was continuous, it suffices for you to perform ablution after the time for prayer begins, and its emission does not invalidate it, similar to someone afflicted with urinary incontinence (sals). You must make up the two missed prayers. The dawn prayer (Salat al-Subh) is valid, and touching does not nullify ablution.