"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.
Is Zakah due on the orphan`s money?
Yes, Zakah is due on the money of the orphan.
What is the ruling on Tarawih prayer?
Tarawih prayer is a confirmed Sunnah (Sunnah Mu’akkadah).
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.