Is it obligatory to perform ghusl and change one's undergarments after every prayer for someone who suffers from continuous discharge? And what is the ruling for someone who feels something discharge after wudu' or while going to the mosque? Should he repeat his wudu' or ghusl?

If the discharge is continuous, such that there is no time for purification and prayer, or if its emission is irregular, then the ruling of incontinence ( سلس ) applies to you. Perform ablution for each prayer after its time has begun and pray as many supererogatory prayers as you wish, taking precautions by tightening a cloth. However, if its emission stops at a known time, then wait for this time, perform ablution, and pray after purifying your clothes and body. And if purifying the impurity is difficult for you, there is no harm in adopting the view of the Malikis, who pardon impurity that exits involuntarily.