Must I repeat the 'Isha prayer if the time for Fajr prayer began while I was performing it, knowing that I have a permanent state of ritual impurity and was unaware of the ruling on invalidating ablution in this case, as well as the ruling on the Adhan before Fajr?

If the Azan (call to prayer) was before Fajr, your prayer is valid and you do not need to repeat it. However, if the time of the Azan was at the emergence of Fajr, then your prayer is invalid and you must repeat it. Some scholars are of the opinion that your ablution (wudu') is not invalidated, and thus your prayer is valid. The Maliki school of thought holds that if an impurity (hadath) is continuous for half or more of the time, it does not nullify ablution, and it is permissible to follow this school when there is a need.