Getting past entity framework BeginTransaction

As the second error message says, Moq can't mock non-virtual methods or properties, so this approach won't work. I suggest using the Adapter pattern to work around this. The idea is to create an adapter (a wrapper class that implements some interface) that interacts with the DataContext, and to perform all database activity through that interface. Then, you can mock the interface instead.

public interface IDataContext {
    DbSet<Repository> Repository { get; }
    DbContextTransaction BeginTransaction();
}

public class DataContextAdapter {
    private readonly DataContext _dataContext;

    public DataContextAdapter(DataContext dataContext) {
        _dataContext = dataContext;
    }

    public DbSet<Repository> Repository { get { return _dataContext.Repository; } }

    public DbContextTransaction BeginTransaction() {
        return _dataContext.Database.BeginTransaction();
    }
}

All of your code that previously used the DataContext directly should now use an IDataContext, which should be a DataContextAdapter when the program is running, but in a test, you can easily mock IDataContext. This should make the mocking way simpler too because you can design IDataContext and DataContextAdapter to hide some of the complexities of the actual DataContext.