Translation:my daughter and my wife
Yes, usually Duolingo does do that. But when one can work out what a word is, eg if we already know word X, and we're given a new word with is X plus a feminine, the new word is likely to be the feminine version of X. I don't think there's any need for a fix, on the contrary.
Just to add, it would have been better if they used ابنتي for my daughter instead of بنتي. The latter sounds more dialectical, and it is derived from بنت which originally means girl.
Bonus: بنت is also used in names, in archaic format (and is still in use in some countries) like stating X daughter of Y, beside X son of Y (similar to the Irish mac and ní).
Yes, this system is still in use in some countries where a male or female has (bin) or (bint) in their names to denote the chain of their fathers (typically only the first and father name are mentioned then family name).
Your example, Fatima bint Mahaa, is correct but usually names are mentioned according to the father line, and Mahaa is a female's name. So it does sound weird a bit. This said, though, there are instances when someone or some group are mentioned by their mother's or grandmother's name for some story maybe or some history behind that. But in usual circumstances, regular names follow the paternal line. In most places the system of bin and bint is dropped and the name is mentioned just by a succession of names like most of the world. I think in Oman they still use the bin and bint system in official naming.
Wife: زوجة (zawjah). My wife: زوجتي (zawjatí).
Husband: زوج (zawj). My husband: زوجي (zawjí).
Worth noting that the word زوجة is relatively a modern Arabic word, because in classical times, the word زوج means the other side of the marriage, whether it's male or female. Technically, it means "pair". However, in modern times, the word زوجة had been invented as a feminine version of زوج to mean "wife" specifically.
You say: "in classical times, the word زوج means (meant) the other side (half?) of the marriage, whether it's male or female. Technically, it means "pair" (couple?)." I would have thought "the other side of the marriage" would not mean "pair", but rather "spouse". A pair means both sides, not "the other side". By "technically", do you mean "strictly speaking"?
Well, I used "pair" here because زوج is used also outside the context of marriage (e.g. shoes). So, it means either 2 of something, or a second part of something. And that also reflects on what I meant by "technically" - I didn't mean strictly speaking, but this is what the word is used for in general I mean, and originally it has no feminine equivalent.
In Quran for example, some verse goes like this:
يا آدم اسكن أنت وزوجك الجنة
(yá 2ádamu uskun anta wa zawjuka al-janna)
(O Adam, settle in paradise, you and your spouse/pair/half/wife).
Here we see زوجك (zawjuka) which would be translated as "your wife" or the equivalent of that even though the word زوج is actually masculine. Also we see here that (zawj) is used for the other part of the bond or another part of something in general - aside from its other usage which can mark 2 of something - e.g. زوج أحذية (zawju aHδiyah) a pair of shoes.
My main point is just to note that "zawjah" زوجة as a word for (wife) did not really exist in Arabic and it's invented in modern times (and some writers and linguists don't like to use it as well)