Scotland will still be part of the EU,
No, it won't still be a part of the EU. As a newly-independent state, it does not inherit membership in any limited-membership treaties. Scotland will have to petition for admission to any such it wishes to join, including the EU. It will then, under EU rules, have to get the unanimous consent of all EU members to join the EU.
I know the SNP says otherwise; the SNP is spouting nonsense.
Now, it's highly likely that the EU will be willing to let it in. However, there's no way it'll be let in without satisfying the rest of Europe on entry conditions.
This is why, in fact, there's no major question on what currency Scotland will use at all. It will either use the Euro from day one or use a local currency locked in the ERM II with the auto-glidepath to joining the Euro, because agreeing to do that will be a condition of joining the EU (nobody has any reason to give the Scots a way to take the Swedish dodge).
Scotland will not get any of the Thatcher-negotiated rebate, because none of the members of the EU have any reason to give it any part; the real wrangling will be between UK-EWNI and France on how much of the Scottish-proportional portion the UK keeps and how much is eliminated.
Scotland will at the same time assume a proportional portion of the British debt, because every EU member looking at its own separatist movement and its own debt will want to make the point to their separatists that independence won't mean escape.