Is it valid to perform Tarawih prayer at home?
It is Sunnah for a Muslim to perform Tarawih prayer in congregation at the mosque.
However, if a person sometimes prays it at home in congregation with their family for a valid reason, there is no harm in doing so.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
What is the ruling on eating and drinking at night after making the intention? Is it necessary to renew the intention?
Eating and drinking at night, even after making the intention (for the next day), does not affect the fast, and it is not necessary to renew the intention after eating and drinking.
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.