Does a discharge of water from the vagina after prayer invalidate ablution and necessitate repeating the prayers? And is prayer waived for a Muslim if it is difficult for him to pray on time due to the unavailability of the conditions of ritual purity?

If you are not certain about what you found on your clothes, whether it came from one of the two private parts, then do not pay attention to it. It is recommended to sprinkle water on the private parts and trousers for anyone afflicted by whispers regarding the emission of an invalidator after performing istinja (definition) (cleansing after relieving oneself). If what is mentioned is continuous for most of the time, then it is a case of سلس (incontinence). Cold water and impure clothes are not an excuse to abandon prayer. What is obligatory is to perform ablution (wudu') or a ritual bath (ghusl (definition)). If one fears harm from using water, then tayammum (definition) (dry ablution) should be performed. If you find no garment except an impure one, pray in it, for covering the 'awrah is more emphatic than removing impurity. You must make up the prayers you missed, and repent and seek forgiveness.