What is the role of the Ka'bah? Why do we pray facing it? Explain the meaning of "House of Allaah". I don't think it means that Allaah lives there.

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.

As for Al-Ka'bah, it is the Qiblah (direction) towards which all Muslims turn their faces while performing prayers, and the first mosque built on earth. Allaah The Almighty Says (what means): {Verily, the first House (of worship) appointed for mankind was that at Bakkah (Makkah), full of blessing, and a guidance for Al-'Alameen (the mankind and jinns).}[Quran, 3:96] It is a duty to turn our faces towards the Ka'bah while praying. Allaah The Almighty Says (what means): {Verily! We have seen the turning of your (Muhammad's) face towards the heaven. Surely, We shall turn you to a Qiblah (prayer direction) that shall please you, so turn your face in the direction of Al-Masjid- al-Haraam (at Makkah). And where so ever you people are, turn your faces (in prayer) in that direction.}[Quran, 2:144]

"The House of Allaah" means that al-Ka'bah was made for Thikr (remembrance) of Allaah The Almighty alone. This does not mean that Allaah The Almighty lives there. He is over the Heavens. In addition, He – in His ultimate wisdom – has the choice to do what He likes, {He cannot be questioned as to what He does, while they will be questioned}[Quran, 21:23]

Allaah Knows best.