Is my son who was breastfed one filling time by my aunt considered a brother to her children?
The baby who was suckled five sporadic times by a woman is considered a son/daughter of hers.
Is it permissible for a woman who is observing `Iddah (waiting period) due to the death of her husband to travel for performing Umrah (Minor Hajj)?
A woman observing `Iddah of a revocable (Rajee`) divorce isn`t allowed to travel for Umrah except with the consent of her husband.
Is it permissible for a person who is in a state of Janabah (Ritual impurity) to clip his nails, or to cut his hair?
It is permissible for those in a state of Janabah and menstruation to clip their nails and to shave whatever hair that is permissible to be shaved. And Allah Knows Best.
Is wearing a cap permissible for boys, or girls?
All Perfect Praise is due to Allah, The Lord of The Worlds.
In principle, anything is permissible sol long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden. And Allah Knows Best.