What exactly does 'Is a woman here?' mean?
In Russian, же́нщина is placed in the beginning of the sentence, so that's why it refers to a known woman. However, I can't say whether this can correspond to 'Is a woman here?' or not because I don't really understand the English sentence. What does it mean?
No, this would be expressed with «Здесь есть женщина?».
You can drop «есть» when existence/presence is not the piece of information you’re trying to convey. In «Женщина здесь?», the main piece of information is given by the word здесь and женщина is someone you and the listener already know (so it’s not the new information). You already knows that there’s some женщина, and you want to know where she is.
In «Здесь есть женщина», the main piece of information is the presence of the woman in a given location, the most important piece of information is есть женщина and здесь just sets the background for the question.
I know my explanation is not ideal, but I can’t explain it better, sorry.
The word order also works similarly: we usually put the most important words in the end (or sometimes in the beginning of the sentence; most notably the question words, but sometimes other words too).
However, word order is tricky because it can be overriden with intonation, so the word order doesn't always help.
It's not too simple to explain because English doesn't have this distinction!
Basically, most consonants in Russian have 2 variants, soft and hard.
Hard is assumed by default or shown by 'non-softening' vowel letter (с /s/, са /sa/, сэ /se/, сы /sɨ/, су /su/, со /so/). Soft is shown either by Ь (сь /sʲ/) or by a 'softening' vowel letter (ся /sʲa/, се /sʲe/, си /sʲi/, сю /sʲu/, сё /sʲo/).
You might want to see YouTube videos about this distinction, or something.