Is wearing a cap permissible for boys, or girls?

In principle, anything is permissible as 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

Is a woman`s face an Awrah (a private part) that should be covered?

During prayer, a woman`s whole body is a private part except the hands and the face. Outside the time of prayer, scholars agree that a woman should put on her Islamic wear to avoid temptation.

Is a woman`s nephew by suckling considered a Mahram( i.e. unmarriageable)who is permitted to accompany her to Hajj?

All that is prohibited by lineage is prohibited by suckling, and a nephew by suckling is a Mahram like a nephew by lineage ;therefore, it is permissible for him to be a Mahram for his aunt in Hajj and Umrah.

Can the Christian widow whose married from a Muslim become an heir of his?