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.
Does an internal medical examination for a woman affect her fast?
An internal medical examination for a woman invalidates the fast because it involves the entry of a foreign object into the body cavity (jauf) while fasting.
In this case, the woman must refrain from eating and drinking for the rest of the day out of respect for Ramadan and make up for the missed fast after Ramadan.
Such an examination should be avoided in Ramadan and other months unless absolutely necessary, as exposing the private parts is only permissible in cases of necessity.
If necessary, a woman should seek a Muslim female doctor first. If one is unavailable, she may see a female doctor from the People of the Book (Jews and Christians). If neither is available, she may consult a trustworthy and competent Muslim male doctor.
What is the ruling on the ablution of one who touches his wife without a barrier?
In the Shafi'i school, a man's ablution is invalidated by touching his wife if their skins meet (in any place) without a barrier, whether the touch is intentional or accidental. An exception to this is touching hair, teeth, or nails; these do not invalidate ablution. And Allah the Almighty knows best.
Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.