If a wajib salat is not offered within its stipulated time period either intentionally or by mistake, then it must be offered as Qaza of that wajib salat. It is a great sin not to offer a wajib salat within its stipulated time period intentionally (thus making it Qaza). There are three types of Qaza of wajib salat:
(a) Qaza salat of your own,
(b) Qaza salat of father on his eldest son,
(c) Qaza salat of a person offered by someone else with or without payment

If you offer a wajib salat in time, but you realise, after the time of that salat has passed, that the salat you offered was void (batil), then you must perform its qaza salat. But if you only doubt that your salat was void, then qaza is not necessary.
A person, having qaza salat due on him, should not be careless about offering them, although it is not obligatory to offer it immediately.
If you have several qaza salat of past days to offer, it is not necessary to maintain sequential order in the offering of those qaza salat. But qaza of Zohr & Asr or qaza of Maghrib & Isha of the same day must be offered in proper sequence. However it is better to maintain order in all qaza salat.
If a person could not offer his wajib salat in time because he was unconscious (or he slept longer by mistake) during the time period of salat, then he must offer it as Qaza salat.
If a woman misses out wajib salat during her monthly menstruation period (Haiz), then she does not have to offer qaza of such salat.
If a kafir becomes a Muslim, he does not have to offer qaza salat for the period he was kafir, because salat is wajib for a Muslim. But if a person was Muslim, then becomes kafir, and then again reverts to be a Muslim, then he has to offer qaza salat of that period he became kafir.
If a na-baligh child, who can distinguish between good and bad, misses out daily salat, then it is recommended for parents to encourage him to offer qaza salat, though salat is not wajib on a na-baligh person.
If you have a large number of wajib qaza salat due on you, but you do not know the exact number of those qaza salat, then you should offer qaza salat of that sufficient number (of days or months or years) which makes you sure that all qaza have been offered.
Lecture #10 Maulana Abul Qasim Rizvi, Panjtan Ctr, Melbourne 19
Normally there is no Qaza of a Mustahab salat. But it is recommended to offer qaza salat of the following Mustahab salat if not offered in time:
(a) Daily Nafila Salat
(b) Daily Salatul Shab

If a person did not offer some of his wajib salat in his life time, then after his death, it is wajib on his eldest son, as ihtiyate wajib, to offer those qaza salat. If he can not do so, then he may hire someone to perform those salat. But if the father left those salat as a deliberate act of transgression, then it is not wajib on the eldest son. Qaza salat of mother is not wajib on eldest son but it is mustahab on the eldest son or her any other child.
If the eldest son doubts whether or not his father had any qaza salat, then it is not wajib on him. If the eldest son knows that his father had certain number of qaza salat due on him, but he is in doubt whether his father offered them or not, then he should offer them as Ihtiyate Wajib. If a dying person makes a will that someone should be hired to offer his qaza prayers, and if the hired person offers them correctly, then there is no obligation on the eldest son. If the eldest son was na-baligh (or insane baligh) at the time of death of his father, then qaza salat of his father is not wajib on him even after he becomes baligh (or becomes sane). If a father had several sons, but his eldest son died during his lifetime, then qaza salat of the father will not be wajib on the next eldest son. If there is a doubt as to who is the eldest son of a person (for example in case of twin boys), then it is not wajib on any son to offer qaza salat of his father. If the eldest son dies before offering qaza salat of his dead father, then offering qaza salat
will not be wajib on the second son.

Qaza salat of a dead person can be offered by someone else on his behalf either on payment basis (ijara) or without payment. He must do Niyyat that he is offering salat on behalf of that person. A male can also offer qaza salat of a dead female, or vice versa.
But qaza salat of a living person can not be offered by someone else on his behalf, even if that person is unable to offer them. However certain Mustahab acts of worship, such as Haj, Umra, and Ziarat can be performed on behalf of a living person if that person is unable to perform.
If the person performing qaza salat of a dead person is under taqleed of a different Mujtahid, and he offers qaza salat according to his own Mujtahid, then such salat is valid.
The person performing qaza salat cannot offer such salat with Tayammum for the dead person, who used to offer his salat with Wudu.
If you hire someone for qaza salat of a dead person, and find out that he was not offering salat correctly, then you must hire another person who offers correctly. But if you doubt that he was not offering correctly, and then he gives assurance about his correctness, and you become satisfied, then it is OK.
If the hired person himself has his own qaza salat, then he should not accept to do qaza salat for another person.
Lecture #10 Maulana Abul Qasim Rizvi, Panjtan Ctr, Melbourne 20