Evidence summary: a report establishes the three initial hand washings after waking; siwak is encouraged at wudu and prayer. Jurists differ about renewing water for repeated mouth/nose rinses, using fresh water for the ears, and the degree of emphasis for beard takhlil.
Finger/toe takhlil is ordinarily sunnah, but can become needed to complete obligatory washing. Three washings are sunnah in form, whereas one proper washing fulfills the fard.