Is it permissible for my father to combine and shorten prayers due to his old age (100 years) and his illness with an enlarged prostate, which causes him continuous dripping of urine, making it difficult for him to perform ablution and change clothes for each prayer?

The descent of a few drops of urine does not necessitate changing clothes; rather, purifying them with water suffices. For someone habitually affected by ritual impurity, the Malikis do not require istinja (cleansing after urination/defecation) or purifying clothes. This does not permit combining prayers unless the discharge is continuous, such that one cannot find enough time to pray with proper purity. In such a case, the person is considered to have incontinence ( سلس ), and the Hanbalis permit combining two prayers, but he is not allowed to shorten them as long as he is a resident.