Is it incumbent on a family to provide for its old handicapped son and take care of him?
The family and relatives - e.g. brothers - of such a person are obliged to spend on him and take care of him if he didn`t have money of his own.
Is it incumbent on the fiancée to obey her fiancé?
When the woman settles in her husband`s house, it is incumbent on him to provide for her and it is incumbent on her to obey him. Before that, and if the marriage contract had been concluded, then she is lawfully his wife and thus she should abide by custom in treating him, but if the marriage contract hadn`t been concluded, then she should treat him as a non-Mahram (Marriageable).
Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
Where should a woman who is led by her husband in prayer stand?
All perfect praise be to Allah The Lord of The Worlds It is from Sunnah (Prophetic tradition) that she stands behind him. And Allah Knows Best.