The best time of Adhkar As-Sabah is after the dawn prayer. However, you can say these Adhkar when you wake up from sleeping, because it is still the time of morning.

There is no proof that the Prophet (peace and blessings of Allah be upon him) said any du`a during wudu whilst washing or wiping his limbs, etc.

With regard to dhikr after salah and before sleeping, you can say: Subhan Allah 33 times, Al-hamdu Lillah 33 times, and Allahu akbar 33 times.