Is the Aqeeqa due on the newborn in case of dying almost a month after the delivery?
Offering Aqeeqa after a week of a newborn death is recommended.
Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.
Is it permissible to divide the Aqeeqah amongst one`s brothers and family?
Giving a portion of the Aqeeqah, even a small one, to the poor and needy is obligatory, and if one`s brothers and family are among the needy then, they are more entitled to it, and this way it is a charity and an observation of kinship ties. However, if they aren`t needy then, it is permissible to give them from the Aqeeqah after giving the poor and needy their share.
I`m a pious Muslim woman, but my husband isn`t, what should I do?
You should exercise patience, make supplication that Allah guides him to the straight path, and keep advising him kindly.