Does moisturizing prevent water from reaching the private parts, and is rinsing with water sufficient to remove impurity, or is it necessary to wash with soap? And how does a woman distinguish between discharges coming from the uterus and those coming from the urinary opening?

If impurity spreads outside the usual place, it must be removed. If there is moisturizer on the spot, the moisturizer must be removed because it has become impure. Then, new moisturizer can be applied after purification. It is not obligatory to remove something whose impurity is doubted. If removing the impure moisturizer causes harm, there is no sin, by analogy with a woman with irregular bleeding (mustahadah) who is not required to bandage herself if it causes her discomfort. Purification does not necessitate the use of soap; rather, washing the area with water until it is highly probable that the impurity has been removed is sufficient.