There is nothing wrong with praying while wearing fake nails, but they should be removed when doing Wudu and Ghusl, so that the water may reach what is beneath them.

If part of the limb that must be washed during wudu remains of the amputated limb, then it must be washed, and in this case it is not acceptable to wipe over the artificial limb, even if it covers the entire arm.

If the beard is light and the skin of the face beneath it can be seen, then it is obligatory to run one’s fingers through it and wash what is beneath it. However, if the beard is thick and the skin of the face beneath it cannot be seen, then it is not obligatory to wash what is beneath it, but it is recommended to run the fingers through it according to the majority of scholars.

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.