First of all, we would like to stress the fact that it has been authentically reported that the Prophet, peace and blessings be upon him, raised his hands in supplication during prayer.
Referring to the first point concerning raising hands while making Du`aa, Sheikh `Atiyyah Saqr, former head of Al-Azhar Fatwa Committee, states the following:
Abu Hurayrah, may Allah be pleased with him, quoted the Prophet, peace and blessings be upon him, as saying: “Allah Almighty is good and accepts only that which is good. Allah has commanded the faithful to do that which he commanded the Messengers, and He Almighty says: “O ye Messengers ! Eat of the good things and do right…”. And Allah also says: “O ye who believe! Eat of the good things wherewith We have provided you…”
Then the Prophet, peace and blessings be upon him, mentioned (the case of) a man who, having journeyed far, is disheveled and dusty and who lifts up his hands to the sky [saying] : “O Lord! O Lord!” – while his food is unlawful, his drink unlawful, his clothing unlawful, and he is nourished unlawfully, so how can he be answered!” (Reported by Muslim)
On the basis of the aforementioned Hadith, most scholars state that there is nothing wrong in raising the hands while making Du`aa.
However, some others state that raising hands is not recommended sunnah while performing Salatul-Istisqaa’ (Prayer performed for beseeching Allah for Rain). They quoted the following Hadith in support of their view:
Anas Ibn Malik, may Allah be pleased with him, reported that the Prophet, peace and blessings be upon him, “did not use to raise his hands in his invocations except in Salatul-Istisqaa’ in which he used to raise his hands so high that one could see the whiteness of his armpits.”
As for rubbing the face after reciting Du`aa, we can say that it is reported by Ibn `Umar, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, “used to rub his face with his hands after reciting Du`aa.” (Reported by At-Tirmidhi)
In their commentary on the previous Hadith, some scholars state that it is a strange or Ghareeb Hadith. Others dubbed it as weak or Da`ief
In his book Al-Adhkar, Imam An-Nawawi, states that there are three different view maintained by the Shafi`is regarding raising the hands and wiping the face while reciting Du`aa. The view which is deemed to be the most correct from among those three opinions is the one which states that raising hands is recommended, whereas rubbing face is not.
To conclude, the issue of rubbing the face after reciting the Du`aa is controversial. Thus, a Muslim can choose the opinion that best suits him in this case.