"The woman speaks no English" is not an accepted solution, even though it is correct (from an English point of view, even if may not be 1to1 translation to Swedish) and the actual translation hints may lead to it.
Edit: I've seen your arguments in other threads, but I still think you should not punish an English translation in a Swedish course, especially at this early stage. Maybe you could accept this answer and add a disclaimer on why this answer is not 100% correct.
Otherwise, amazing job, big thanks for all the hard work!
The point is that "speaks no English" has a much different meaning than "is not speaking English" and it is pretty important to know that "talar inte Engelska" means the latter. "Inte" is purely a negative modifier on a verb and does not modify the noun. Later, there will be Swedish words, such as "ingen" used to modify the noun in the same way that "no" modifies the word English in "speaks no English."
hi aranworld, consider also the semantic difference between " is not speaking english" with "does not speak english". the first might rightly be be interpreted as not speaking english right now (at the moment), although does speak english at other times. the later would probably be thought of in general as not knowing how to speak english. what do you think?
I think this website provides some good background on it: http://blogs.transparent.com/swedish/to-speak-in-swedish-tala-prata-snack/
In short, "talar" is a bit dry and informal. In English, for example, it might be better to say "the school girls chatted with each other" instead of "the school girls spoke with each other." You would not say "talar" to refer to what you did on the phone with your best friend; "pratar" would be a better word. You might use "talar" to describe what a teacher did when scolding a child who was constantly late to class.
Kvinnan talar inte engelska = The woman is not speaking English or The woman does not speak English.
If it is said with the English definition "The woman is not speaking English" (1) implied, then that is different than "The woman can't speak English" (2)
(1) implies that she is currently not speaking English regardless of if she is capable of it or not (2) specifies that she doesn't have the ability.
To specify that the woman does not have the ability to speak English, (The woman can't speak English),
You would say "Kvinnan kan inte talar engelska."
"The woman is not speaking English" is not the same as "The woman does not speak English."
If my bilingual child who could speak both Swedish and Norwegian was at the playground speaking in Swedish, and a woman asked me "Is he speaking Norwegian?" I could then answer, "He is not speaking Norwegian."
If I were to say, "he does not speak Norwegian," then it would indicate that my child did not have the ability to speak Norwegian just the same as if I said, "he can not speak Norwegian," or "he speaks no Norwegian."