What is the ruling on the prayer of one who has continuous vaginal discharge and cannot renew her ablution outside the home? And what should she do if she feels the discharge coming out during prayer while she is at home? Is it permissible to wear a pad during prayer?

These secretions nullify ablution according to the Four Imams. If these secretions stop for a sufficient time to perform ablution and prayer, then you must perform ablution and pray within that time. However, if they do not stop, or do not cease for a sufficient period, then you are among those with an excuse, like a woman experiencing istihada (non-menstrual vaginal bleeding). In this case, you should perform ablution for each prayer after its time has begun, and the emission of anything during prayer will not invalidate it. If you perform ablution before the prayer time begins and something is emitted, your ablution is nullified according to the majority of scholars. There is an opinion among the Shafi'is that it is not nullified as long as you have not yet performed the prayer for which you made ablution. What is obligatory upon you is to perform ablution for each prayer after its time has begun. If that is difficult and you perform ablution before the time begins, it is hoped that this will suffice you. Placing a sanitary pad does not prevent these emissions from nullifying ablution.