An appropriate single word simply won't be found. The closest you might come would be "manna from Heaven" but that refers to food alone; nothing else.
It might help if you could clarify the contrast between "… the word 'gift' isn't listed in my bilingual dictionary…" and "I looked up the word in my bilingual dictionary and the translation I'm looking for is…"
Most things sent by God would be blessings, although some would be curses.
If you want good things given, blessings seems close… but anyone can give a blessing. It doesn't have to come from God…
Broadly, curses are not "given" but "inflicted" but that's probably a different topic.
Any person might well be "favoured" by God but that person might much more likely be "favoured" by another mortal; as with blessings, "favours" can come from anyone; not solely from God.
"Thanks/owing/due to" and "profitable, doing well (of anyone or thing)" in no way need to relate to God. Small amounts of food taken home after ceremonial meals would more likely be stolen from the temple than given by God.
As in your opinion, the first part of the first sense from those four is more appropriate and more likely to be used.
The "context" you give, by the way, will never work.
Andy: What do you think of my eyes? The doctor said it's strabismus. Causing bad luck! this makes my appearance less attractive and no girl will be attracted to me!
That so clearly doesn't work even in English, it looks more than likely to be an unnatural construction even in the language it came from.
Lucy: Hey! You should be grateful for the blessings given by God! Some people were born with blind eyes.
That does show the context but it also shows similar translation problems. What works, there, is solely "blessings". Native English speakers would tend more to "God's blessings" or "the blessings of God" than "the blessings given by God."
So no, none of that sounds natural.
When the word "gift" crops up in subtitled anime, please remember there's a great difference between "I'm familiar with…" and "I've come across…" or "I've seen/heard/read…"
Nice hair or whatever else, "It's a gift" works in that scenario and might well be short for "… a gift from God…" but it doesn't at all have to mean that. Either way, the context is too specific for the meaning to be applied generally.
("I confuse which word…" should probably be "I am confused about which word…")