Right usage of ViewModels in MVC

I'm new to MVC and i'm having some difficulty on understanding the proper usage of ViewModels and Controllers.

I have this example where i will list several different informations in my HomeController as CTAs, Banners, News, Courses... and i came up with this ViewModel structure after some research :

public class CoursesViewModel
{
    private readonly Entities _db = new Entities();
    public List<Courses> Courses { get; private set; }

    public Courses ViewModel() { Initialize( "", "", 0 ); }

    public CursosViewModel( string where, string order, int take ) { Initialize( where, order, take ); }

    private void Initialize( string where, string order, int take )
    {
        IQueryable<Curso> query = _db.Curso;

        if( !string.IsNullOrEmpty( where ) )
            query = query.Where( @where );

        if( !string.IsNullOrEmpty( order ) )
            query = query.OrderBy( @order );

        if( take > 0 )
            query = query.Take( @take );

        Courses = query.ToList();
    }
}

public class BaseViewModel
{
    private readonly Entities _db = new Entities();

    public Page Page { get; private set; }
    public List<State> States { get; private set; }
    public List<HtmlBlock> Blocks { get; private set; }

    public Page GetPage( int pageId )
    {
        return Pagina = _db.Page.FirstOrDefault( x => x.ID == pageId ) ?? new Page();
    }

    public void SetBlocks( Page page )
    {
        Page = page;
    }

    public void SetBlocks( List<HtmlBlock> blocks )
    {
        Blocks = blocks.OrderBy( x => x.Ordem ).ToList();
    }

    public void SetStates( List<State> states )
    {
        States = states;
    }
}

And this is my Controller:

public class HomeController : Controller
{
    private readonly Entities _Db = new Entities();

    [MinifyHtml]
    public ActionResult Index()
    {
        var HtmlParser = new HtmlParser();
        var Redirect   = HelperMethods.GetRouteRedirect( HttpContext );
        var BaseVM     = new BaseViewModel();

        var page = BaseVM.GetPage( Redirect.pageId );

        if( page == null ) return new TransferResult( "/not-found" );

        //My ViewModel calls happen inside the HtmlParser.ParseBlocks,
        //there i will get the right ViewModel to each View and instantiate it
        BaseVM.SetBlocks( HtmlParser.ParseBlocks( page.html, ControllerContext ) );
        BaseVM.SetStates( ViewBag.states );

        return View( BaseVM );
    }
}

Is this the correct "usage" for the ViewModel and Controller ? Should i use my Entities (_db) inside a closure ( using ) ? Why ?

Another thing, i have some common information that exists on every page, how can i work with this on ViewModels without repeating the properties on each ViewModel. I created a BaseViewModel, should i extend it on every ViewModel or should i implement it as a property ?