Some of the scholars stated that seeking refuge with Allah – by saying “A‘udhu Billahi min ash-shaytan ir-rajim (I seek refuge with Allah from the accursed Shaytan) – before doing wudu is recommended (mustahabb). But the hadiths which describe the wudu of the Prophet (blessings and peace of Allah be upon him) – of which there are many – make no mention of seeking refuge with Allah when starting to do wudu, and the scholars who stated that it is recommended did not quote any hadith to prove that. This indicates that the Prophet (blessings and peace of Allah be upon him) did not do that, and the best of guidance is the guidance of the Prophet (blessings and peace of Allah be upon him). For more details, please see the long answer.

It is not essential to remove the braces when making Wudu because rinsing the mouth means making water move around in the mouth and this can be done when the braces are there.

Continuity in Wudu means one should not delay washing any part for so long that the part that was washed before it becomes dry, within an average timespan. So, simply opening the door and the like is not regarded as an interruption that would nullify doing the actions consecutively. But if one is distracted by something else that leads to a lengthy interruption during Wudu, then in this case he should start his Wudu anew.