What is the ruling regarding someone whose bed and covers have become ritually impure due to dryness, and who experiences urine dripping for half an hour after urinating? Is it sufficient for him to perform istinja’ for the urine dripping instead of re-purifying [his clothes/body]? And why must a person afflicted with سلس (urinary incontinence) perform wudu’ for every prayer? And is it permissible to perform tayammum instead of ghusl?

Nothing becomes impure due to doubt. If the impure object is dry, the impurity does not transfer from it. However, if it is wet or damp, the impurity does transfer, and this is the prevalent ruling. If the matter becomes difficult for you, you may adopt the easier opinion. If by "ghusl" you mean purification from urine impurity, then ghusl is not obligatory for you; rather, it is sufficient to purify the parts of your body or clothing to which the impurity has transferred. You can also designate specific clothes for sleeping. Tayammum is only permissible when water is unavailable or one is unable to use it. Istinja' is sufficient for urine drops. However, if the discharge is continuous, the person is afflicted with incontinence (sals), and they have specific rulings.