Is it permissible for a wife to give her money to her family as a charity, or a gift without asking her husband, or seeking his consent?
The wife has the right to give her money as a charity, or a gift to her family, or to other people after consulting her husband out of respect, and this is the meaning of treating on footing of kindness and equity. Therefore, if he wanted to stop her from helping her family, then there is no harm in not telling him.
Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
Is it permissible for a woman to adorn herself with kohl (eyeliner) and go out wearing it?
Kohl is a form of adornment, and it is forbidden for a woman to display her adornment to anyone other than her husband or a Mahram. And Allah Knows Best.
What is the ruling on obtaining a house through the King Abdullah II project (Decent Housing for a Decent Living), knowing that we do not own a house, our financial situation is moderate, our current rental costs are high, and we are eight people living in the household?
If owning the apartment/house is done through the same institution/project then it is permissible, but if this took place through usurious banks then it is impermissible, since dealing with usurious transactions is unlawful. And Allah Knows Best.