What should one who made an intention, at night, to make up for a missed fasting day, but broke his fast on the next day?
One who started making up a missed fasting day, then broke his/her fast without a legitimate reason is considered sinful, and is only obliged to make up for the missed fasting days. 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 one who sees moisture on his clothes and doubts whether it is semen or pre-seminal fluid (madhy)?
Whoever finds moisture upon waking from sleep and doubts whether it is semen or madhy, and cannot distinguish between them, he may choose between them and act according to his choice. If he wishes, he can consider it semen and perform the ritual bath, or consider it madhy, perform ablution, and wash what it has soiled. This is because if he fulfills the requirement of one of them, he is definitively free from it, and the default is his innocence from the other. And Allah the Almighty knows best.
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.