What is the ruling on swimming while fasting?
Swimming while fasting is disliked (makruh) due to the risk of water entering the body cavity (jauf) through the nose, ears, or mouth, which would break the fast.
Ramadan is a month of tasbeeh (glorifying Allah), not Sibaha (swimming).
What should a person, who doubts the validity of his Wudu, or over performs it, do?
One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.
Do ear and nose drops break the fast?
Yes, ear and nose drops break the fast because both the nose and ears are open passages to the body cavity.
What is the ruling on entering the toilet with something containing the remembrance of Allah?
It is disliked to bring into the toilet anything containing a reminder of Allah, such as the Quran or a sacred name (like the name of Allah, Muhammad, etc.). If one does that, etiquette dictates that he conceal it so it is not visible while entering the toilet, either by cupping his hands over it, putting it in his pocket, or inside his shirt if it is a necklace or ring. And Allah the Almighty knows best.