Russian nouns (and adverbs) have several forms.
Она́ is the Nominative case form. Nominative case is used for subjects of the sentence: Она́ программистка. (She's a programmer.)
Неё is a Genitive case form used after certain prepositions.
Yes, among other things. «Де́ньги бра́та» 'bother's money' describes the possession.
Would you need to say "Программистка?" I read that adding the -ка, although it does refer to a woman, that it may be seen as an insult. Also, saying someone is just a "программист" should imply merely their title. I do not know though, it just seems easier to equate the person to the profession without the use of gender-based endings.
«Она программист» is correct, too.
Russian femininst suggesting using more feminine words for professions (because the existing words are not really gender-neutral, they’re masculine, and when we hear the word программист, we do imagine a male person, and this reinforces our stereotypes), and I’m trying to follow that recommendation.
If it’s easier for you to use masculine words, this is correct, too.
«Неё» is used after prepositions (unless it's a possessive pronoun, as in «у её сестры́»). All non-possessive pronouns beginning with е- get н appended after the prepositon.
Isn't asking if she has water possessive?
It's conveys a possessive meaning, but without using a possessive pronoun.
«Her water» = «её вода́» uses a possessive pronoun, «her»/«её».
But «the water she has» = «вода, которая у неё есть» doesn't use a possessive pronoun. Neither does «у неё есть вода?» = 'Does she have water?'. Here, possession is conveyed using the verb 'to have' in English, or using the preposition «у» in Russian, and not using a possessive pronoun.
The sentence «у её сестры есть вода» 'her sister has water' actually has a double possessive meaning: "She has a sister. That sister has water." But the possession in 'her sister' is conveyed using a special variant of pronoun, and in 'has water' it's conveyed without using possessive pronouns.
This is a highly idiomatic sentence. The bare statement, У неё есть вода means "by her is/exists water".
У is a multi-purpose preposition which here = "by/near", and неё = "her" is the object of this preposition.
Because there is a question mark, the words have to be rearranged in English to make the sentence a valid question: У неё есть вода? = "by her is there water?"
That's not very good idiomatic English, so the question is loosely translated (or transformed) into "Does she have water?"
Why неё and not она?
Objects of the preposition у must be put into genitive case, and неё = "her" is the genitive case form for она = "she" (nominative case).
Why неё and not её?
In a declination table of pronouns, you will find genitive "her" = её. However, under the rules of Russian grammar, н is prefixed to её when it follows a preposition. In general, if the object of a preposition is a pronoun beginning with a vowel, you add н to the pronoun (prefixed, or put at the beginning of the word).
NOTE: A table listing nouns or pronouns whose endings vary according to case, gender and/or number is called a "declination table", similar in concept to "conjugation table" for verbs.
NOTE: The case of prepositional objects depends upon which preposition is involved (and whether motion is involved). Not all such objects are cast in genitive case by any means. But that will come later.
To Russian speakers, they sound different. Неё /nʲɪ'jo/ has a Й sound, and него /nʲɪ'vo/ has a В sound.
It might be hard to hear because different languages have different sound systems, so when your brain tries to apply your native sound system to other languages, the results are not always ideal. But the difference is there.
Because does takes the -s ending (that's why it's does and not do), and not have.
«У» is a preposition introducing possessor. I.e. literally the sentence is like "At her [possession, there] is water".
In speech, by a rising intonation in questions and falling intonation in statements (I agree this might be different with the automated voice). In writing, by a full stop vs. a question mark at the end.
It's not even that ‘got’ is understood, it's simply a construction of its own that means the same thing, using the good old verb-subject inversion to phrase questions from statements. It comes across as archaic to many English speakers these days, but it still sees regular use in Scotland and Ireland, if not elsewhere.
That said, if you want it to be considered an acceptable variant, you need to manually report it using the Report A Problem button when you reach that question - this is how alternative translations are added to the database.