What is the ruling on the prayer of a woman into whose vagina enter the waters of istinja' and then exit at intermittent intervals, despite her efforts to avoid that, and is the exiting water considered impure and does it nullify wudu'?

What is obligatory upon a woman in istinjāʾ (cleansing after relieving oneself) is to wash the outer vagina, without letting water reach its inner part. Any water remaining on the outer vagina after purifying the impurity is pure, and its exiting onto clothes does not have an effect. If you doubt whether water reached the inner vagina, the default assumption is that it did not. Do not pay attention to waswās (whispers/obsessive thoughts), for giving in to them leads to great evil.