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 tasting food while fasting?
Tasting food while fasting is disliked (makruh). However, if any part of the food reaches the body cavity (jauf), the fast becomes invalid.
Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?
The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.
Someone wiped over his shoes after wearing them in a state of purity, then took them off and prayed without them?
Ablution is not invalidated by taking off leather socks or shoes after wiping over them. However, whoever takes them off after wiping must wash his feet only. If he prayed without washing his feet, he must wash his feet and repeat the prayer. And Allah the Almighty knows best.