These are difficult problems without a good answer. Will the smaller independent nations be able to provide a better answer to these problems? I seriously doubt they will.
In the case of the euro crisis smaller independent nations have already proven that they can. The UK is not in the euro, it was hit as bad if not worse than any other EU nation during the financial crisis but because it still retained control of its currency and had a functioning central bank it has dealt with that crisis while the flaws of the euro are still unresolved and have effectively been brushed under the rug.
Make no mistake, if the EU had competently dealt with the issues with the euro the UK would not have left.
USA, Australia, Canada, Japan ... all had their challenges with immigration and fiscal/monetary issues and have been able to find suitable solutions without their federation/country falling apart.
