Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
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.
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).
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.