Are these people obliged to fast? Are they obliged to make up the fast?

The people mentioned in the question do not all come under the same ruling. We have mentioned the difference of opinion among the scholars and some of their words in the answer to question no. 49008. 

We can divide the people mentioned in the question into two categories: 

The boy who reaches puberty, the kaafir who becomes Muslim and the insane person who regains his sanity come under the same ruling, which is that they must refrain from eating and drinking for the rest of the day, but they do not have to make up the fast. 

As for a menstruating woman who becomes pure, the traveller who settles and the sick person who recovers, they come under one ruling, which is that they do not have to refrain from eating and drinking, and they do not benefit at all from doing so, but they have to make up the fast. 

The difference between the first and second groups is that the first group attains the conditions of being obliged to fast, namely being an adult, being a Muslim and being sane. Once it is proven that they are obliged to fast, then they must refrain from eating and drinking, but they do not have to make up the fast because they refrained when it became obligatory for them to refrain, and before that they were not obliged to fast. 

As for the second group, the command to fast is addressed to them so it was obligatory in their case, but they had excuses which made it permissible for them not to fast, namely menses, travel and sickness, so Allaah granted them a concession and allowed them not to fast. The sanctity of the day was waived in their case, but when their excuses ceased to exist during the day, they would not benefit from refraining from eating and drinking, but they have to make up that day after Ramadaan ends. 

Shaykh Muhammad ibn Saalih ibn ‘Uthaymeen (may Allaah have mercy on him) said: 

If a traveller reaches home and he is not fasting, then he is not obliged to refrain from eating and drinking, and he may eat and drink for the rest of the day, because refraining will not benefit him in any way, as he is required to make up this day. This is the correct view and it is the view of Maalik and al-Shaafa’i, and it is one of the two views narrated from Imam Ahmad (may Allaah have mercy on him). But he should not eat and drink openly. End quote. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen (19/question no. 58). 

He also said: 

If a woman who is menstruating or bleeding following childbirth becomes pure during the day, she does not have to refrain from eating and drinking, and she may eat and drink, because refraining will not benefit her in any way, as she is obliged to make up that day. This is the view of Maalik and al-Shaafa’i, and it is one of the two views narrated from Imam Ahmad. It was narrated from Ibn Mas’ood (may Allaah be pleased with him) that he said: “The one who ate at the beginning of the day, let him eat at the end of it” i.e., if it was permissible for him to eat at the beginning of the day, it is permissible for him to eat at the end of it too. End quote. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 19/question no. 59. 

The Shaykh was also asked: 

If a person does not fast during the day in Ramadaan for a legitimate excuse, is it permissible for him to eat and drink for the rest of the day? 

He replied: 

It is permissible for him to eat and drink, because he broke the fast for a legitimate excuse, and if he broke the fast for a legitimate excuse, then the sanctity of the day does not apply in his case, and he is allowed to eat and drink, unlike a man who breaks the fast during the day in Ramadaan with no excuse; in his case we say that he is obliged to refrain from eating and drinking, even though he is obliged to make it up. Attention must be paid to the difference between these two cases. End quote. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 19/question no. 60. 

He also said: 

During our discussion on fasting, we stated that if a woman is menstruating then she becomes pure during the day, the scholars differed as to whether she is obliged to refrain from eating and drinking, or whether it is permissible for her to eat and drink for the rest of the day. We say that two views have been narrated concerning that from Imam Ahmad, one of which – which is the well-known view of the madhhab – is that she must refrain from eating and drinking. The other view is that she does not have to refrain, and it is permissible for her to eat and drink. We say that the second view is the view of Maalik and al-Shaafa’i (may Allaah have mercy on them), and this is what is narrated from Ibn Mas’ood (may Allaah be pleased with him), because he said, “The one who ate at the beginning of the day, let him eat at the end of it”. And we say that what the seeker of knowledge must do with regard to matters concerning which there is a difference of opinion is to look at the evidence, and to adopt the view which he believes to be most correct and not to pay attention to any other opinion so long as he has evidence, because we are enjoined to follow the Messengers, as Allaah says (interpretation of the meaning):

“And (remember) the Day (Allaah) will call to them, and say: ‘What answer gave you to the Messengers?’”

[al-Qasas 28:65]

With regard to quoting as evidence the saheeh hadeeth in which the Prophet (peace and blessings of Allaah be upon him) issued the command to fast ‘Ashoora’ during the day, and the people refrained from eating and drinking for the rest of the day, we say: they have no evidence in this hadeeth, because fasting the day of ‘Ashoora’ is not like a case when the reason for not fasting ceases to exist. Rather it is confirming the obligation of fasting. There is a difference between the cessation of a reason not to do something and confirmation that something is obligatory, because what confirming that something is obligatory means is that the ruling that it is obligatory was not there before, whereas the cessation of a reason not to do something means that the ruling is established but there is a reason not to follow it. 

A similar case would be if a kaafir became Muslim during the day. If a person becomes Muslim the obligation is confirmed for him. And a similar case is if a boy reaches puberty during the day when he is not fasting; the obligation is confirmed for him. So we say to the one who became Muslim during the day: you have to refrain from eating and drinking, but you do not have to make up this day. And we say to the boy who reached puberty during the day: you have to refrain from eating and drinking, but you do not have to make up this day. This is unlike a menstruating woman who becomes pure; in that case the scholars are unanimously agreed that she has to make up that day. If a menstruating women becomes pure during the day, the scholars are unanimously agreed that if she refrains from eating and drinking for the rest of the day, that will not benefit her and it will not count as fasting, and she has to make up that day. Hence we can see the difference between confirmation of the obligation and the cessation of a reason not to do something. If a menstruating woman becomes pure, this comes under the heading of the cessation of a reason not to do something, and if a boy reaches puberty or, as the questioner mentioned, the fasting the day of ‘Ashoora’ was enjoined before fasting Ramadaan was enjoined, this comes under the heading of confirmation of obligation. And Allaah is the Source of strength. End quote.

Majmoo Fataawa al-Shaykh Ibn ‘Uthaymeen, 19/question no. 60.