All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The excellence to which you referred in the question about staying (sitting) in one’s prayer place after the Fajr prayer until after sunrise and then praying two Rak’ahs, is something proven by the saying of the Prophet, sallallaahu ‘alayhi wa sallam: “Whoever prays the Fajr prayer in congregation and then he remains sitting mentioning Allaah until the sun rises, and then he prays two Rak’ahs, will receive the reward of one Hajj and one ‘Umrah. The narrator said: the Prophet, sallallaahu ‘alayhi wa sallam, said ''Complete, complete, complete.” [At-Tirmithi graded it as Hasan (good) and Al-Albaani agreed with him]
This reward is for every day and not restricted to someone who observed this act of worship throughout his entire life.
As regards the multiplication of this reward to 70 times during the month of Ramadan, then we are not aware of any evidence about it. However, there is a Hadeeth about the multiplication of the reward of obligatory acts of worship but the chain of narration of the Hadeeth is not authentic. Ibn Khuzaymah reported a long Hadeeth in his Saheeh about the excellence of Ramadan, which reads: “… whoever does an optional act of goodness in it (Ramadan) in order to get closer to Allaah, will be like a person who performed an obligatory act of worship in other times, and whoever performs an obligatory act of worship in it, will be like a person who performed 70 obligatory acts of worship in other times.” (The same Hadeeth was reported in some other books of Hadeeth).
Some scholars, including Ibn Hajar and Al-Albaani graded this Hadeeth as Dha’eef [weak]. The evidence for this is from Ibn Khuzaymah who wrote a Chapter about this Hadeeth which he entitled: ‘The Chapter of the Excellence of the Month of Ramadan if the Hadeeth is Authentic’.
Hence, some scholars hold the opinion of multiplying the reward of the good deeds according to the mentioned detail pursuant to this Hadeeth. In any case, there is no doubt that an act of obedience in the month of Ramadan is of virtue and its reward in this month is multiplied, but as far as we know there is nothing authentic from the Prophet, sallallaahu ‘alayhi wa sallam, about the specification that you mentioned in the question. For more benefit, please refer to Fatwa 160215.
On the other hand, it is permissible to gift the reward (of a good deed) to your parents or to other Muslims and they will benefit from it, Allaah willing. We have already clarified the permissibility of gifting the reward of acts of obedience, by which one seeks to get closer to Allaah, to the deceased as in Fataawa 84938 and 131592.
As regards whether or not you still get a reward after gifting the reward to your parents, then some jurists state that the person who gifts (the reward of a good deed) is expected to get a reward and he is not excluded from the reward due to gifting. They also said that both the person who gifts and the one who is being gifted get a reward; as the Bounty of Allaah is so vast.
However, it is also probable that if a person does an act of worship by which one gets closer to Allaah and then he gifts its reward to others, that it is the person to whom this reward was gifted who gets the reward and there is nothing left to the one who gifted it, as he was pleased by gifting that reward to the deceased person. Anyway, he gets a reward for being kind to the deceased person, especially if the latter was his father or mother.
Allaah Knows best.