In this context, when there is a woman right there, speaking at the moment but in another language than English. Hon talar inte engelska refers more to her language skills, whether she is actually talking right now or not.

Att prata = to talk Att tala = to speak

Prata is the more casual form of Tala. It's that simple. :)

The main rule is the V2 rule: In any sentence (except questions and subclauses) the finite verb needs to be in second place. The finite verb is the one that can show time (like, I sing - I sang, sing/sang are finite verbs. In 'I love to read', love is a finite verb, but not read).

With very few exceptions, yes. :) One exception to be something like "I can't make her if she doesn't want to" - "Jag kan inte tvinga henne om hon inte vill" OR "If you don't do this, you're fired" - "Om du inte gör det här blir du avskedad".

But in simple sentences like this in the beginning of the course, it's safe to assume that "inte" comes after the verb. You'll probably learn the exceptions further down the road.

No, the language 'English' is only called engelska in Swedish, in the noun form. Engelsk is used as an adjective, e.g. en engelsk bok, 'an English book', but never as a noun.

We don't capitalize the words for days of the week, months, languages or nationalities in Swedish – basically we only capitalize names.

Then it would have to be She does not speak/is not speaking in English in English too.

The words for languages normally end in -a. The language Swedish is svenska for instance.