Is what comes down after the yellowish discharge the white discharge, knowing that it usually does not come down until after 15 days?

The maximum duration of menstruation is fifteen days. As long as the duration of your menstruation, including any yellow or brownish discharge connected to it, does not exceed fifteen days, then all of that period is considered menstruation. If you doubt the occurrence of purity (ṭahārah), the default is that menstruation persists. You should rely on this principle until you are certain of achieving purity, either by seeing dryness (the cotton swab comes out clean) or by seeing the white discharge (al-qaṣṣah al-bayḍā’).