Can you kindly explain in depth the conditions and the number of rak'ahs to be prayed for fardh and Sunnah prayers while combining Salah?

There are two types of combining prayers; one is called jam'u taqdeem where one Salah is joined with the other Salah and performed before its due time. For example, a traveler will perform Zuhr and ‘Asr at the time of Zuhr. Similarly he or she will pray Maghrib and Isha at the time of Maghrib. The other type of combining is called jam'u ta'kheer where the prayer is combined with another prayer and performed after its due time has passed like in the case of Zuhr which will be performed with ‘Asr at the time of Asr. Similarly, in this scenario, Maghrib will be performed with Isha at the time of Isha.

In the shortened prayer, a person performs two rak'ah for Zuhr, ‘Asr and Isha. The number of rak’ah for Maghrib does not change in the journey; it remains the same. The Sunnah for the traveler is not to pray the nafil salah, except for the two rak’ahs before Fajr which the Prophet (ﷺ) used to perform.

But an exception is made from the above in the case of the regular Sunnah prayer of Fajr, which is to be performed when travelling just as it is performed when one is not travelling. Ibn al-Qayyum said:

“It was the practice of the Prophet (ﷺ) when travelling to pray only the obligatory prayers, and it was not narrated that he used to pray the regular Sunnah prayers either before or after the fardh prayers, apart from Witr and the Sunnah of Fajr, which he never omitted whether he was travelling or not.” [1]

It was narrated that Abu Qutaadah  said: “The Prophet (ﷺ) was on a journey and the Messenger of Allah (ﷺ) stopped to rest and I stopped with him. He (ﷺ) said, ‘Look!’ I said, ‘Here are one rider, two riders, and three…’ until there were seven of us. He said, ‘Make sure that we do not miss our prayer’–meaning Fajr prayer. But they slept deeply and nothing woke them but the heat of the sun. Then they got up and travelled on for a while, then they stopped and did wudu’, and Bilaal gave the adhaan and they prayed two rak’ah of Fajr then they prayed Fajr, then they rode on. They said to one another, ‘We have been negligent concerning our prayer.’ The Prophet (ﷺ) said, ‘There is no negligence in sleep, rather negligence comes when one is awake. If one of you forgets his prayer, let him pray when he remembers.’” [2]

In the chapter called Kitaab Salat al-Musaafireen wa Qasriha (The Prayer Of Travelers And Shortening The Prayer) (no. 724), Imam Muslim narrates from ‘Aa’ishah (radiAllahu anha) that the Prophet (ﷺ) was not more keen to pray any nafil prayers regularly than the two rak’ah before Fajr.

Similarly, it is prescribed for the traveler to continue to pray Witr, qiyaam al-layl (nafil prayers at night), Zuhr prayer and all prayers done for a reason such as praying after each wudu’, Salat al-Tawba (prayer of repentance), tahiyyat al-masjid (greeting the mosque), two rak’ahs following Tawâf, etc. Similarly, it is not forbidden to pray nafil at all.

This is indicated by the following hadith:

1. It was narrated that Abu Hurayrah said: “My dear friend [the Prophet] enjoined three things upon me which I will not give up whether I am travelling or not: two rakats of Zuhr prayer, fasting three days of each month and not going to sleep until I have prayed Witr.” [3]
2. It was narrated that Ibn ‘Umar said: “The Prophet (ﷺ) used to pray qiyaam al-layl atop his camel when he was travelling, no matter what direction it was facing, gesturing to represent the movements of the prayer, apart from the obligatory prayers, and he would pray Witr atop his camel.”[4] According to another report: “The Messenger of Allah (ﷺ) used to pray nafil prayers atop his camel, no matter what direction it was facing, and he would pray Witr like that too, but he did not pray the prescribed prayers like that.” [5]
3. It was narrated that Jabir ibn ‘Abd-Allah said: “The Messenger of Allah (ﷺ) used to pray atop his camel, no matter what direction it was facing, but when he wanted to pray an obligatory prayer, he would dismount and face the qiblah.” [6]

References:

[1] Zaad al-Ma’aad, 1/473

[2] Narrated by Muslim, 681

[3] Sahih Sunan Abi Dawood, 1269

[4] Narrated by al-Bukhaari, 1000

[5] Narrated by al-Bukhaari, 1098

[6] Narrated by al-Bukhaari, 400

[7] Narrated by al-Bukhaari, 357