What is the ruling on pouring a small amount of water on the place of urination, and is the spot considered pure, and does the hand become impure when touching things afterwards?

If you are not certain that impurity has touched a part of your body, then the original state is purity, and neither your hand nor what it touched is ruled impure. As for impurity touching a child, if you pour water on the impure spot until you are reasonably sure that the impurity has been removed, then its removal is ruled valid; for reasonable certainty is sufficient in purifying impurities. One must not give in to obsessive doubts in this matter.