Some native speakers cannot say these Rs, so you won't be alone. You can swallow most of them, and try to cheat some other way with the rest. – It'll sound less like an accent if you use for instance a y sound like in 'yes', than if you use English r:s. – To use a v sound instead is a classical stereotype about nobility.
Say hello to the V2 rule which will be a dear friend of yours as long as you study Swedish :)
In normal Swedish sentences (= not questions and subclauses), the verb needs to go in the second place in the sentence. It doesn't necessarily have to be the second word, since a part of the sentence can consist of several words. Like, Boken är röd or Den stora boken är röd essentially have the same structure.
Anyway, the verb needs to go in the second place, and since it's odd to have inte first, it really has to go after the verb here.
Sorry this took me so long. Apparently I had a two-week sinusitis bout rather than just a slight cold, so my voice has been off for what feels like ages.
Anyway, please find a recording and an explanation at http://duolingo.vydea.io/39d99924bf0c403ea0059118638086f2.mp3
I answered "It is not raining" and got it correct. Duolingo tells me that "Another correct solution" to "Det regnar inte." is "It does not rain" - is this accurate? In English "It is not raining" and "It does not rain" would mean two different things, but is this something that context determines in Swedish? Is there a better way to clarify that it's currently not raining versus it never (or rarely, if we're not exaggerating) rains?