Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
What is the ruling on insulin injections?
Insulin injections do not break the fast because they are administered under the skin and do not reach the body cavity (jauf).
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
If a woman becomes pure from menstruation shortly after Fajr in Ramadan, what is required of her?
If a woman becomes pure (from menstrual period) after Fajr, even shortly after, it is recommended (but not obligatory) for her to refrain from eating and drinking for the rest of the day. However, she must make up for that day after Ramadan.
She will be rewarded for both refraining from eating (imsak) and making up the fast (qada) since she was menstruating for part of the day.