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.
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.
What is the ruling on fasting for those with diabetes, heart disease, high blood pressure, kidney disease, or ulcers?
● A sick person who is completely unable to fast is exempted from fasting and must offer fidyah (feeding a needy person), as Allah Almighty says {what means}: "and [in such cases] it is incumbent upon those who can afford it to make sacrifice by feeding a needy person." [Al-Baqarah/184]. They are not required to make up for the missed fasts.
● A sick person who can fast on some days but not others should fast when able and make up the missed days after Ramadan when possible. No fidyah is required in this case.
● If fasting during the long, hot summer days is too difficult for a sick person, but they can make up the fasts during the shorter, cooler winter days, they should break their fast and make up for it when they are able, without fidyah.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.