And he may cling to the place between the corner and the Door - placing his chest and face and forearms upon this place. 
And there is no particular dhikr for tawaf - so he may read Quran or say any dhikr he pleases, according to the Prophet's saying : Tawaf around the House is prayer, except that Allah has allowed speech in it, so he who speaks then let him not say except, good things and in a narration : so let him limit his talk in it.” 
And it is forbidden for a naked person or a menstruating woman to make tawaf of the House, as he said: A naked person may not make tawaf of the House.”  And his saying to ‘Aa'ishah when she came to make ‘Umrah in the final Hajj : Do as anyone making Hajj does, except do not make tawaf of the House (and do not pray) until you become clean. 
So when he finished the seventh round he covers his right shoulder and moves to the Place of Ibrahim and recites: Wattakhidhu min-maqami ibrahima musalla.
And take ye the Station of Abraham as a place of prayer.
[Noble Quran 2:125]
And he places the Maqami Ibrahim (Place of Abraham) between himself and the Ka'bah and then prays two rak'ahs.
And he recites therein Surat-ul-Kafirun and Surat-Qul Huwallahu Ahad.
And he should not walk between the hands of any praying person there, nor allow anyone to walk in front of him while he is praying - as the ahadith forbidding that are general - and there is no established exception for the Haram Masjid, let alone the rest of Mecca. 
Then after praying he goes to Zamzam and drinks thereof, and pours some of the water onto his head, as he said: “Zamzam water is for what it drunk for”  and he said “It is blessed and it is a food and a cure for illness”  and he said: The best water upon the face of the earth is Zamzam water, in it is nourishment and a cure from illness. 
Then he returned to the Black Stone, says takbir and touches it - as before.