What is the ruling on praying Dhuhr late and Asr prayer without a new ablution due to a yellow discharge from the sensitive area? And is it permissible to go to the mosque for 'Ishaa prayer and attend the lesson despite the mother delaying the prayer?

If the discharge of fluid is continuous such that it does not cease, the questioner should perform ablution for each prayer after its time has begun and take precautions, then whatever is discharged will not harm her. It is permissible to delay the Dhuhr prayer if it does not lead to its time expiring, such as waiting for the congregation. As for the Asr prayer with the same previous ablution, if nothing is discharged, scholars have differed on its ruling. There is no sin upon a woman for going to the mosque for prayer if the conditions are met, and she may perform supererogatory prayers and listen to lessons even if she is not in a state of ablution (unless she is in a state of major ritual impurity or menstruation), but it is better for her to perform prayer in her home.