What is the ruling on seeking out prayer and supplication at the pillars of the Prophet’s Mosque, such as "Aisha's Pillar"? And what is the ruling on supplicating for the intercession of the Prophet (peace be upon him) and to drink from his Hawd (pond) at his grave? And what is the ruling on seeking out supplication at the Multazam of the Kaaba?

The questioner has done well by hitting upon the Sunnah in seeking to pray at the pillar where the Prophet, peace and blessings be upon him, used to seek to pray. This is the perfumed pillar (Al-Ustuwana Al-Mukhallqa), also known as the Pillar of the Muhajireen or the Pillar of Aisha.

As for supplication (dua), there is no harm in a Muslim asking his Lord to grant him the intercession of the Prophet, peace and blessings be upon him, anywhere in the mosque. He should direct his supplication towards the Qiblah, not towards the grave. The imams have agreed that one should not face the grave when making supplication.

As for supplication at the Multazam, scholars have deemed it commendable, and there are narrations regarding its virtue, some of which are considered good (hasan) by their aggregate.