Can't access base properties in derived class (C#)

I'm having trouble with inheritance/polymorphism in C#/Xamarin.Forms. There's multiple things I'd think I would be allowed to do, but I'm not, and from what I gather it seems I'm not inheriting correctly, so first things first:

Declarations

public abstract partial class CommonCell : ContentView, ICellSection
{

    public static readonly BindableProperty TitleProperty = BindableProperty.Create("Title", typeof(string), typeof(CommonCell), default(string));
    public string Title
        {
            get { return (string)GetValue(TitleProperty); }
            set { SetValue(TitleProperty, value); }
        }
    public CommonCell()
            : base()
        {

        }
    public virtual IInputType GetInputType()
        {
            throw new NotImplementedException();
        }
}

In the same file i also declare this derived class:

[XamlCompilation(XamlCompilationOptions.Compile)]
public partial class CellSection<T>: CommonCell where T : View, IInputType
{
    private T _inputType;
    public T InputType
        {
            get { return _inputType; }
            set { _inputType = value; } //plus more stuff here
        }
    public CellSection ()
            :base()
        {
            //Layout Initialization
        }
    public override IInputType GetInputType() //I get an error here (Problem 2)
        {
            return InputType;
        }
}

I've only included one property and one method to demonstrate my problem, but there are many more declared the same way...

Problem 1

What happens is that when I create a new CellSection, like this:

CellSection<TextInput> section1 = new CellSection<TextInput>();
section1.Title = "New Title"; //This line is not allowed

I'm not allowed to access the Title property...

Error message: CellSection<TextInput>' does not contain a definition for 'Title'

I've been able to access it by adding the following code to the CellSection<T> class:

public string Title
    {
        get { return base.Title; }
        set { base.Title = value; }
    }

but this seems so damn unnecessary and redundant... There must be another way...

Problem 2

The other problem I have is that I'm not allowed to override the virtual method GetInputType(), it is in the code above as well, but this is the line I'm talking about:

public override IInputType GetInputType()
{
    return InputType;
}

Error message: 'CellSection<T>.GetInputType()': no suitable method found to override

Problem 3

The final problem is that when I'm, from a different class/file, attempt to reference/cast a CellSection<T> to ICellSection (which is implemented by the base class CommonCell)

List<ICellSection> Sections = new List<ICellSection> { section1, section2 };

I get an error that it's not allowed.

Error message: Argument 1: cannot convert from 'CellSection<TextInput>' to 'ICellSection'

This one I'm more unsure about as I don't know if it's even possible (can't find examples on it), but the problem 1 and 2 I just don't understand why won't work as they seem pretty straight forward...