1. Late at night
At a certain time of the night, as the Prophet (peace and blessings of Allaah be upon him) said: “During the night there is a time when the Muslim does not ask for the good of this world and the Hereafter but it will be given to him, and that happens every night.” Narrated by Muslim, 757.
2. A certain time On Friday
The Messenger of Allaah (peace and blessings of Allaah be upon him) mentioned Friday and said: “During it there is a time when a Muslim slave does not stand and pray and ask Allaah for something, but He will give it to him,” and he gestured with his hand to indicate how short that time is. Narrated by al-Bukhaari, 935; Muslim, 852. See also question no. 21748.
3. At the Crowing of a Rooster
Abu Hurairah (RA) narrated that the Prophet (SAW) said: ‘When you hear a rooster crowing, then ask Allah for His bounties, for it has seen an angel, and when you hear a donkey braying, then seek refuge in Allah from Shaitan, for it has seen a Shaitan’ [Sahih al-Bukhari, Muslim, Ahmad, Sahih al-Jami #611]
“When you hear the crowing of a rooster, ask Allaah of His bounty, for he has seen an angel.” Narrated by al-Bukhaari, 2304; Muslim, 2729.
4. While visiting the sick, and dua made by the sick
Ali (RA) reported that the Prophet (SAW) said: ‘When a Muslim visits his sick Muslim brother in the morning, seventy thousand angels make dua for his forgiveness till the evening. And when he visits him in the evening, seventy thousand angels make dua for his forgiveness till the morning, and he will be granted a garden for it in Jannah.’
[at-Tirmidhi, abu Dawud]
5. Dua immediately after wudu
Umar ibn Al-Khattab reported that the Prophet (SAW) said: ‘There is not one of you that makes wudu, and does it perfectly, then says: I testify that there is no deity worthy of worship except Allah. he is Alone, having no partners. And I bear witness that Muhammad is His slave and messenger’, except that the eight gates of Paradise are opened for him, and he can enter into it through whichever one he pleases’ [Muslim #234, abu Dawud #162, Ahmad, an-Nasa’i]
for part one…..