Praise be to Allah.
It is permissible to drink standing and sitting, but drinking whilst sitting is preferable.
It says in Fataawa al-Lajnah ad-Daa’imah (22/133):
The basic principle is that one should drink sitting down, and this is preferable, but one may drink whilst standing. The Prophet (blessings and peace of Allah be upon him) did both, to demonstrate that the matter is broad in scope. End quote.
With regard to facing towards the qiblah whilst drinking, no hadith has been narrated from the Prophet (blessings and peace of Allah be upon him) concerning that.
The fuqaha’ (may Allah have mercy on them) regarded it as mustahabb to face towards the qiblah when drinking Zamzam water, and they quoted as evidence for that the report narrated by Ibn Maajah (3061) from Muhammad ibn ‘Abd ar-Rahmaan ibn Abi Bakr who said: I was sitting with Ibn ‘Abbaas, and a man came to him and he said: Where have you come from? He said: From Zamzam. He said: Did you drink from it as you should? He said, How is that? He said: When you drink from it, turn to face the qiblah and mention the name of Allah, drink three draughts and drink your fill of it. When you have finished, then praise Allah. The Messenger of Allah (blessings and peace of Allah be upon him) said: “The sign (that differentiates) between us and the hypocrites is that they do not drink their fill from Zamzam.”
It was classed as da‘eef by Shaykh al-Albaani (may Allah have mercy on him) in Da‘eef Sunan Ibn Maajah.
See also: al-Mawsoo‘ah al-Fiqhiyyah (1/91)
The hadeeth quoted above is da‘eef, as stated, hence the more correct view is that it is not mustahabb to face towards the qiblah whilst drinking, whether one is drinking Zamzam water or anything else.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Some of them said: … and he should face towards the qiblah. But this is da‘eef, because the Prophet (blessings and peace of Allah be upon him) drank Zamzam water and it is not narrated that he faced towards the qiblah (whilst doing so).
End quote from ash-Sharh al-Mumti‘ (7/348)
And Allah knows best.