Question comes: "What are some rulings concerning fasting? For instance, while traveling or on a journey or while under extreme conditions?"
The authentic Sunnah states that Allah's Messenger traveled during the month of Ramadan for the battle for Makkah. The Prophet marched until he reached the area of Kadid and then broke his fast and ordered those who were with him to do likewise. This was recorded in the Two Sahihs. Breaking the fast mentioned in this Hadith was not required, for the Companions used to go out with Allah's Messenger during the month of Ramadan, then, some of them would fast while some of them would not fast and neither category would criticize the others. If the command mentioned in the Hadith required breaking the fast, the Prophet would have criticized those who fasted. Allah's Messenger himself sometimes fasted while traveling. For instance, it is reported in the Two Sahihs that Abu Ad-Darda' said, "We once went with Allah's Messenger during Ramadan while the heat was intense. One of us would place his hand on his head because of the intense heat. Only Allah's Messenger and `Abdullah bin Rawahah were fasting at that time.''
We should state that observing the permission to break the fast while traveling is better, as Allah's Messenger said about fasting while traveling:
«مَنْ أَفْطَرَ فَحَسَنٌ، وَمَنْ صَامَ فَلَا جُنَاحَ عَلَيْه»
(Those who did not fast have done good, and there is no harm for those who fasted.)
In another Hadith, the Prophet said:
«عَلَيْكُمْ بِرُخْصَةِ اللهِ الَّتِي رُخِّصَ لَكُم»
(Hold to Allah's permission that He has granted you.)
Some scholars say that the two actions are the same, as `A'ishah narrated that Hamzah bin `Amr Al-Aslami said, "O Messenger of Allah! I fast a lot, should I fast while traveling'' The Prophet said:
«إِنْ شِئْتَ فَصُمْ، وَإِنْ شِئْتَ فَأَفْطِر»
(Fast if you wish or do not fast if you wish.)
This Hadith is in the Two Sahihs. It was reported that if the fast becomes difficult (while traveling), then breaking the fast is better. Jabir said that Allah's Messenger saw a man who was being shaded (by other people while traveling). The Prophet asked about him and he was told that man was fasting. The Prophet said:
«لَيْسَ مِنَ الْبِرِّ الصِّيَامُ فِي السَّفَر»
(It is not a part of Birr (piety) to fast while traveling.) This was recorded by Al-Bukhari and Muslim.
As for those who ignore the Sunnah and believe in their hearts that breaking the fast while traveling is disliked, they are required to break the fast and are not allowed to fast.
As for making up for missed fasting days, it is not required to be consecutive. One may do so consecutively or not consecutively. There are ample proofs to this fact. We should mention that fasting consecutive days is only required exclusively during Ramadan. After the month of Ramadan, what is required then is to merely make up for missed days. This is why Allah said:
﴿فَعِدَّةٌ مِّنْ أَيَّامٍ أُخَرَ﴾
(. ..the same number (should be made up) from other days.)