"If the fidyah becomes obligatory upon a pregnant or nursing woman because she broke her fast out of fear for her child, is it obligatory from her own wealth, or from her husband's wealth?"
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The fidyah (ransom/compensation payment for breaking the fast) is obligatory from the wife's own wealth, and is not obligatory upon the husband unless he voluntarily chooses to pay it on her behalf.
It is stated in Mughnī al-Muḥtāj (Vol.2/P.174): "If the two [the pregnant woman and the nursing mother] fear for the child alone — such as a pregnant woman fearing miscarriage, or a nursing mother fearing that her milk supply would decrease, thereby endangering the child — then both the qaḍā' (making up the missed fast) and the fidyah become obligatory upon them, to be paid from their own wealth." And Allah, the Exalted, knows best.
Does excessive sleep during Ramadan invalidate fasting?
Sleeping a lot in Ramadan does not invalidate the fast, but a Muslim may miss out on great rewards from prayer, Quran recitation, and acts of worship due to excessive sleep.
What is the ruling on wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.
What is the ruling on using eye drops while fasting?
Eye drops do not break the fast, even if the taste reaches the throat, because the eye is not an open passage to the body cavity.