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. And Allah Knows Best.

Is it permissible for one to shake hands with his uncle`s daughter?

No, it isn`t because he is a non-Mahram (Marriageable) to her.

Should the father command his ten-year-old daughter to wear the Islamic dress?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

The father should order his daughter to put on the Islamic dress once she turns ten, in order for her to get used to it. And Allah Knows Best.

What is the ruling on making up for missed fasting after the second half of Sha`ban (the month before Ramadhaan)?

One is obliged to make up for missed fasting before the start of next Ramadhaan, and regardless of offering it during the first, or the second half of Shab`an. This is because the prohibition mentioned in the Hadith is for offering absolute voluntary fasting in the second half of Sha`ban. And Allah Knows Best.