Is it permissible to say the recommended Dua during Wudu in the bathroom that consists of a toilet, shower, and sink? Is it permissible to say Allah's names or Salawaat in such a bathroom?
Yes it is permissible to recite Du'a and mention the name of Allah everywhere. We have a Hadeeth stating that Prophet Musa asked Allah: Can I mention your name when I am in a place where I feel ashamed to do so? Allah replied: O Musa, mention my name everywhere.
It is recommend to recite Sura Al-Qadr during performing Wudhu where ever you perform Wudhu.
Wassalam.