What is the ruling on the liquid that appears on the male organ after lying down, and is it obligatory to perform Istinja (washing) and Wudu (ablution) from it, or is Istijmar (cleaning with stones/tissue) sufficient?

This is a severe case of waswas (obsessive whispering/doubts), and the cure for waswas is to ignore it. The Maliki jurists have made matters easy regarding impurity for those from whom it exits without their control. You may act upon their madhhab (school of thought) due to the ease and alleviation it provides, and it will remove hardship from you in purifying impurity, which is often an illusion and waswas. As for wudu' (ablution), it is only obligatory upon certainty of the exit of something that necessitates it. A person afflicted with incontinence is not required to perform wudu' for every prayer according to the Malikis, and you may adopt this opinion as it is easier for you. If the impurity has dried, it is sufficient to pour water over its location. The matter is easy, so do not give in to waswas.