Membership of the EU is a question the only the UK Government can provide an answer to, and they are unwilling to do so. However, there is absolutely no reason why the EU would refuse membership to Scotland. In reality we would be fast tracked in.
We will use the pound, until Scotland either establishes it's own currency or joins the Euro, there is no question of that.
The oil industry is privatised, the Scottish Government would collect taxes on it the same way that the UK Government collects taxes.
Norway is not an EU member by the way, they also have their own currency. The SNP have released their manifesto of how they see an independent Scotland, that does not mean that an indepenent Scotland will follow the SNP's vision. Other independent Scotland's are available and you will get to vote on them in these things called elections.