Is it permissible for a woman to sit with her brothers-in-law?

It is impermissible for a woman to sit with her brothers-in-law, and it is also impermissible for a person to have a Khulwa (seclusion) with his sister-in-law.

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.

What is the ruling on someone who doesn`t perform prayer?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                    Not performing prayer is a major sin, and one who doesn`t pray out of laziness is considered an oft-sinner ;whereas, the one who denies that it is mandatory is considered a disbeliever. And Allah Knows Best.

Does the wife have the right to stop her husband from visiting some of his relatives because their meetings involve religious violations?

Couples should advise one another in kindness, and the wife can stop her husband from committing sin by resorting to a kind and tactful approach.