What does the pilgrim (Hajj) and the 'Umrah performer intend when visiting the Prophet's Mosque, and are there specific etiquettes for visiting the Prophet's Mosque?

One who intends to visit the Prophet’s Mosque should intend to visit the Mosque, not the grave. Upon entering, one should mention Allah’s name and send prayers upon the Prophet (peace be upon him). It is preferable to pray in the Noble Rawdah. Then, one should stand before the noble grave and greet the Prophet (peace be upon him) with politeness and reverence. After that, one should turn to the right and greet Abu Bakr and Umar (may Allah be pleased with them both). It is not permissible to wipe the Prophet’s Chamber, circumambulate it, or face it when supplicating. A woman should not visit the grave of the Prophet (peace be upon him) or any other grave; rather, she should pray and send greetings upon him from her place. It is commendable for men to visit Al-Baqi’ and greet its inhabitants, and to visit Mount Uhud and reflect on the events of the غزوة (battle).