What should a person, who doubts the validity of his Wudu, or over performs it, do?
One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.
Is it permissible to openly announce the engagement of a woman who is in her waiting period (iddah)?
It is not permissible to openly announce the engagement of a woman in her waiting period (Iddah), but it is permissible to hint (imply) at it if she is in her waiting period after the death of her husband. And Allah Knows Best.
Is it permissible to add the nutmeg to one`s food?
All Perfect Praise is due to Allah, The Lord of The Worlds
Using a little bit of the nutmeg for seasoning is permissible, but using a great deal of it is impermissible since it could lead to intoxication, and Islam has forbidden all intoxicants and stupefacients. And Allah Knows Best.
What is the ruling on going out wearing a long loose skirt with a long shirt that are neither tight nor revealing and without wearing any makeup?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
This is permissible as long as it doesn`t attract the attention and isn`t considered adornment, and this varies according to the environment in which you live. And Allah The Almighty Knows Best.