Вы можете добавить панель инструментов во Фрагменты, используя это
((YOUR_ACTIVITY) getActivity()).getDelegate().setSupportActionBar(toolbar);
1: up to you; you can't really do anything about them, so I'd probably let them surface unless I needed to hide it from the caller (replacing it with a similar, less specific exception)
2: You should keep connections as "local" and short-lived as possible; often one per method call. Most providers have connection pooling, meaning you will get back the same underlying connection (as long as you use the same connection string), without having to stress about synchronization, re-entrancy, etc (it will allocate more connections as needed)
3: look at patterns like the repository pattern; look also at ORM frameworks like LINQ-to-SQL, Entity Framework, NHibernate, etc.
i.e.
Customer GetCustomer(int id) {
using(var conn = CreateConnection()) {
conn.Open();
// etc
}
}
Only advice I would give you is that this has been done before by people a lot smarter than myself, and they've learned from the pitfalls. Perhaps your time would be well spent reading over what frameworks are available for you to customise as opposed to rolling your own code?
Other than that I would recommend that you think hard about the consumer of your db layer, make sure that they don't need to know what the hell is going on inside your layer to work out what to do. Make a friendly reusable public interface and this should help you significantly.
I'd also recommend that you have a close look at Linq to SQL as utilising this would make your class library look a whole lot different, as opposed to staying with ADO.net or a vanilla ORM.