Is removing feces with water and hand together considered a proximity to forbidden impurity, and if not, what is the sufficient method for Istinja’ (purification after defecating or urinating) from feces and urine without using the hand? And is the method of Istinja’ with water-wipes sufficient, using a new wipe for each swipe?

It is permissible to use the hand for istinja' (cleaning oneself after defecation or urination) with water, and there is no harm in it. This is better than relying solely on stones because it is more effective in cleansing, and this is the opinion of most jurists. As for istijmar (cleaning oneself with stones or similar dry objects), it is a condition that the stone or tissue used be dry. If it is wet or damp, it will become impure, and then it will make the area impure. In such a case, using water afterwards becomes obligatory to remove the impurity.