The times when the Prophet (peace and blessings of Allah be upon him) made du`a during Hajj and ‘Umrah
Question

What are the times when the Prophet (peace and blessings of Allah be upon him) made du`a during his Hajj and ‘Umrah?.
Praise be to Allah.It should be noted that the pilgrims who are performing Hajj and ‘Umrah are guests of Allah, a delegation who have come to Him. Allah has not invited them except to be generous to them and honour them. 
According to a saheeh hadeeth: “The warrior who fights for the sake of Allah, and the pilgrim performing Hajj or ‘Umrah are guests of Allah Who invited them and they responded to Him; they asked of Him and He gave that to them.” Narrated by Ibn Maajah; see al-Silsilah al-Saheehah, 1920. 
The greatest gift that He has given to them – and all His gifts are great – is that they will go back (free of sin) as on the day their mothers bore them, after having come weighed down with a heavy burden of sin. They will not end their pilgrimage and rituals except they will come out freed from that burden of sin, coming back by the mercy of Allah and His pleasure, after having being guests of the Most Generous, Most Merciful. 
According to a saheeh hadeeth: “Whoever comes on pilgrimage to this House and does not utter any obscenity or do any evil action, will go back free of sin as on the day his mother bore him.” 
Glory be to Him, how great and majestic He is! All these records which were filled with sins will be cancelled out, because of the steps that the Muslim took to reach the House of Allah. What a journey it is, and whoever misses it cannot claim that he has gained anything, and whoever does it cannot lose anything. The Prophet (peace and blessings of Allah be upon him) said: “An accepted Hajj brings no less a reward than Paradise.” 
With regard to the times when the Prophet (peace and blessings of Allah be upon him) made du`a during Hajj and ‘Umrah, they are as follows: 
1 – du`a at al-Safa. It is narrated in the lengthy hadeeth narrated by Jaabir (may Allah be pleased with him) describing the Hajj of the Prophet (peace and blessings of Allah be upon him) that he started with al-Safa and climbed until he could see the Ka’bah, then he turned to face the qiblah and proclaimed the Oneness of Allah and magnified Him, and said: “Laa ilaaha ill-Allah wahdahu laa shareeka lah, lahu’l-mulk wa lahu’l-hamd wa huwa ‘ala kulli shay’in qadeer; laa ilaaha ill-Allah wahdahu, anjaza wa’dah wa nasara ‘abdah wa hazama al-ahzaaba wahdah (There is no god but Allah alone with no partner or associate, His is the dominion and to Him be praise and He has power over all things; there is no god but Allah alone, He fulfilled His promise, granted victory to His slave and defeated the confederates alone).” He said this three times. Narrated by Muslim, 1218. 
2 – du`a at al-Marwah. In the hadeeth referred to above, it says: Then he came down to al-Marwah, until when his feet reached the bottom of the valley he ran, until he came to al-Marwah, and he did at al-Marwah as he had done at al-Safa. Narrated by Muslim, 1218. 
3 – du`a at al-Mash’ar al-Haram, as narrated in the hadeeth quoted above: “Then he rode al-Qaswa’ (his camel) until he came to al-Mash’ar al-Haram, where he turned to face the qiblah and said du`a and magnified [Allah] and proclaimed His Oneness, and he remained standing there until it had become very light.” Narrated by Muslim, 1218. 
4 – du`a on the day of ‘Arafah. The Prophet (peace and blessings of Allah be upon him) said: “The best of du`a is on the day of ‘Arafah.” Narrated by al-Tirmidhi, 3585; classed as hasan by al-Albaani in Saheeh al-Jaami’, 4274. 
5 – du`a after stoning the smallest and middle Jamarahs. Al-Bukhaari narrated in his Saheeh from Saalim ibn ‘Abd-Allah that ‘Abd-Allah ibn ‘Umar (may Allah be pleased with them both) used to stone the closest Jamarah (al-Jamarah al-Dunya) with seven pebbles, saying takbeer after each throw, then he would proceed until he reached the level ground, then he would stand facing the qiblah for a long time, making du`a and raising his hands. Then he would stone the middle Jamarah likewise, then he would move to the left towards the level ground, and stand facing the qiblah for a long time, making du`a and raising his hands. Then he would stone Jamarat al-‘Aqabah in the bottom of the valley, and he would not stand by it, and he would say: ‘This is what I saw the Messenger of Allah (peace and blessings of Allah be upon him) doing.’ Narrated by al-Bukhaari, 1752 
And Allah knows best.