About the whole "EU citizenship" thing - here is how it works, because an awful lot of guff has been expressed by the Yes camp.
The EU is a creation of treaty entered into by its member states.
The European Commission and EU parliament are created under these treaties. Accordingly, their powers are limited to those conferred on them by treaty.
EU citizenship is thus also a creation under treaty.
Under international law, a country that secedes from another state walks away from all treaties entered into by the previous state, unless it is a "continuing state". It is easy to see the logic of this - why should State A, who has entered into a treaty with State B suddenly be obliged to deal with State B1 without having any say in the matter?
Anyway. A "continuing state" won't include Scotland. Accordingly, it won't be party to any of the EU treaties and thus will have to apply for membership. This has a number of ramifications. First, under the current rules, any new entrant has to adopt the Euro. Second, the existing states have to approve membership. Spain, which has its own secession issues on its hands might say no. The rump-UK might say yes only if a deal was cut - examples being the continued stationing of nuclear weapons on Scottish soil, or a cut of the oil revenue. Finally, it also means that Scottish citizens wouldn't be EU citizens unless a deal was struck allowing them to remain UK citizens.
FWIW, and this is another point entirely, there hasn't been a king or queen of Scotland or England since 1707. Both kingdoms were abolished by the Acts of Union. However, HM is also queen of NZ, Australia, Canada and other places too. Scotland would just be added to the list - no big deal at all.