What is the ruling on swearing on the Holy Quran and breaking that oath?
It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
Does collecting saliva and swallowing it break the fast?
Swallowing collected saliva does not break the fast, but it is an unnecessary and meaningless act.
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.