It is a confirmed sunna to brush one’s teeth every time one performs wudu, optimally with a miswak. The place for this is when one washes ones mouth.
It is recommended to pray 2 rakats afterwards during non-disliked times. Given this, one would not pray this during the 3 prohibited times:
as the sun is rising after fajr time is over,
just before zuhr time enters,
and towards the end of Asr time, when the sun’s rays dim such that one can look towards it without being dazzled.
It is also disliked to pray any nafl prayers
After Fajr time comes in, except the 2 rakats of the sunna of Fajr, After praying the fard of Fajr,
After praying the fard of Asr,
After Maghrib time enters, until one has prayed the fard,
After the khutba has commenced for the Friday prayer (or effectively, if the khatib has risen on the minbar).
In these times, if one enters the masjid, one simply sits down, and does not pray the 2 rakats of greeting the mosque. (One should intend it with the next prayer one performs, though.)
Similarly, one cannot pray Salat al-Tawba (the prayer of repentance) or Salat al-Istikhara during these times. (One should simply recite the dua itself, if in a hurry, or wait until a non-disliked time.)
And Allah alone gives success.
By Shaykh Faraz Rabbani