Is a woman`s neck an Awrah (private part)?
All Perfect Praise is due to The Lord of The Worlds.
It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams (Marriageable men). And Allah Knows Best.
My mother inherited a share from my late father`s and brother`s property; however, the inheritance, a piece of land, wasn`t divided amongst the eligible heirs because it was hard to sell. While alive, she used say that she wanted these shares to be distributed amongst the poor and needy. What is the ruling of Sharia on this?
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.
This is a will, so we have to consider the estate she had left behind. If the piece of land, which she had willed, equals one third and less of her estate, then the will must be executed. But, if it is more than one third, then one third must be executed and the rest of the estate, if the heirs agreed, is to be executed as part of her will as well. However, if the heirs haven`t approved of that, then what remains, excluding that one third, must be divided amongst them according to the Islamic rules of inheritance. Moreover, we recommend that you pay a visit to the Iftaa` Department to make things clearer for you. And Allah The Almighty Knows Best.
Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
Is it permissible for a woman to go out wearing bright colors?
Bright colors are part of a woman`s adornment, and it is impermissible for her to show it to people other than her husband, or one of her Mahrams (Unmarriageable kin).