What is the ruling on smoking?

All Perfect Praise is due to Allah, The Lord of The Worlds

Smoking is forbidden (Haram) since it is harmful to one`s health as confirmed by trustful physicians, and Islam has forbidden taking anything that causes harm. The Prophet (PBUH) said: "There should be neither harm nor reciprocated harm." [Ibn Majah and Ahmad]. And Allah Knows Best.

What is the semi-circular structure abutting the Holy Kabah?

It is the Black Stone of the Holy Kabah, and one should pass from behind it while offering Tawaf(circumambulation) because it is part of the Kabah.

Is the `Iddah (waiting period) of the divorced effective from the time the divorce took place, or from the time of registering it at the court?

It is considered effective from the time the divorce took place, and not from the time of registering it at the court.

Is it permissible for a woman to pluck her eyebrows, or to shave them and have a tattoo in their place?

It is forbidden for a woman to pluck her eyebrows, or to shave them and have a tattoo in their place since this is called (Nums), and the Prophet (PBUH) has cursed those who do it.