All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Yes, it is permissible to use braces on the teeth and this does not affect the validity of ablution or Ghusl (ritual bath), even if they prevent the water reaching the teeth because rinsing one's mouth and nose is a Sunnah in ablution and Ghusl according to the majority of scholars. Although one who does not rinse his mouth and nose at all, his purification is correct and acceptable. Even the scholars who are of the view that rinsing the mouth and nose is an obligation when performing ablution or Ghusl, like the preponderant view of the Hanafi school, they still do not consider that it is a condition that water has to reach all the parts of the mouth and nose, but they only consider this as desirable. Ibn Qudaamah said: "It is not an obligation to rinse all the mouth and nose, as this is only desirable for someone who is not fasting." As regards the scholars who are of the view that this is an obligation in Ghusl and not in ablution, and they are the Hanafi school, they have stated that it is an obligation that water reaches all the parts of the mouth and nose. The author of Rad Al-Muhtaar said: 'Rinsing the mouth means that water should reach all the parts of the mouth, but they excluded the parts that are difficult to rinse.'
Therefore, it is not an obligation to wash what is under the braces because of the hardship and difficulty of doing so, whether that is in ablution or in Ghusl. It is enough to rinse the braces of the teeth as Allaah says (which means): {And has not laid upon you in religion any hardship.}[Quran 22:78]. Allaah further says (which means): {Allaah burdens not a person beyond his scope.}[Quran 2:286]. Indeed, one of the established rules by the scholars is that when there is a difficulty in a given matter the easiest permissible method is taken towards it and that hardship necessitates easiness.
As regards making up for missed prayers, one has to make them up immediately and not wait for the same time the next day as the Prophet said: "Whoever sleeps and misses a prayer or forgets to pray it, its expiation is to pray it as soon as he remembers it.", and then he recited the saying of Allaah (which means): {And perform the prayer for My Remembrance}[Quran 20:14] [Al-Bukhari and Muslim].
The author of Az-Zaad said: 'The missed prayers should be immediately performed in sequencing order.' Shaykh Al-Islam Ibn Taymiyyah said 'Whoever sleeps or forgets a prayer has to perform it as soon as he remembers it, and that is its time [the time he is obliged to perform it] and if he again delays it without a sound excuse, he is sinful in the same way a person who delays performing an obligation immediately.'
Allaah Knows best.