Is it obligatory to combine prayers when outside the home due to inability to change clothes because of discharge or uncertainty about its purity, or is it sufficient to perform ablution for each prayer and offer it at its prescribed time without changing clothes?

These secretions, known as vaginal discharge, are pure (tahira) and do not necessitate combining prayers. You only need to perform ablution (wudu') from them, without needing to purify the body or clothing. If their discharge is continuous, such that it does not stop for a time sufficient for purification and prayer, then your ruling is that of one afflicted with perpetual discharge (sahib al-salas). In this case, you perform ablution after the time for prayer begins and pray as much as you wish until that prayer time exits.