Hajar al-Aswad (The Black Stone), which is set in the eastern corner of the Ka’bah. Tawaf is started and ended by facing this sacred stone. Throughout the ages, innumerable people including many of the Prophets (alaihi al-salam), Prophet Muhammed (Salla Allahu alaihi wa sallam) Himself, Sahabah’s (radi Allah anho), Pious personalities and millions of Muslims whom have performed Hajj and Umrah have placed their blessed lips on it.
1) Special consideration must be taken when one intends to kiss the Hajar al-Aswad. One should neither push others nor harm anyone and must remember even though it is Sunnah to kiss Hajar al-Aswad it is also forbidden (haram) to cause harm or be hurtful towards others. When the area is crowded, it will suffice to merely point towards the Hajar al-Aswad with ones hand or a stick while reciting the Takbeer and then to kiss the hand or stick. Although the Prophet (Salla Allahu alaihi wa sallam) kissed the Hajar al-Aswad directly, He (Salla Allahu alaihi wa sallam) also pointed towards it when the area was crowded, it is therefore clear that both kissing it and pointing towards it are Sunnah.
It is in Hadith – Narrated by Naafi’: I saw Ibn Umar touch the Stone with his hand then he kissed his hand. He (Ibn Umar) said, I have never ceased to do this since I saw the Messenger of Allah (Peace be upon Him) do it. (Sahih Bukhari & Muslim).

2) The Hajar al-Aswad was brought from Jannah and presented to Ibrahim (alaihi al-salam) to be placed on the corner of the Ka’bah. Ibn ‘Abbas (aradi Allah anho) narrated that the Prophet (Salla Allahu alaihi wa sallam) said: “The Black Stone came down from Paradise. [Tirmidhi]

3) Du’as are accepted at the Hajar al-Aswad.