Does an internal examination require ghusl?
Ghusl isn't required for making internal examination; however, it invalidates one's fasting. And Allah Knows Best.
Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
What is the ruling on having slight discharges of menstrual blood during daytime of Ramadan, and before Maghrib time?
A woman who is certain that her menses have started during daytime of Ramadan is in a state of menstruation, and her fasting is considered broken at first sight of blood. However, she is rewarded for not breaking fast at the beginning of daytime.
What should a woman, who has given several births during different months of Ramadhaan, and didn`t make up for them in addition to forgetting the exact number of the days and years in which she had missed fasting, do?
She should make up the missed days of Ramadan after estimating their number, and paying the ransom (in food) due on each missed day that she had delayed making up. In addition, she is obliged to repay the ransom according to the number of years if she was able to fast before that time, but didn`t.