Is it possible for instance to destroy/delete self?

No, there is no way to achieve what you are trying to do in C#.

If you consider an example :

public class Kamikadze {

     ......             
     private void TimerTick(..) 
     {
        ....
        if(itsTime) {
            DestroyMe();
        }
     }

     .....
}


var kamikadze = new Kamikadze ();

after a while DestroyMe() will be called that cleans internal data.

But the reference kamikadze (pointer if you wish) is still valid and points to that memory location, so GC will not do anything, will not collect it, and instance of Kamikadze will remain in memory.

C++: If an object was allocated dynamically, it can delete its this pointer in its own function, provided the this pointer is never used again after that point.

Your question is very interesting, and I don't know of any other way to do so in C# but to force from the inside of the instance its destruction from the outside. So this is what I came up with to check if it is possible. You can create the class Foo, which has event that is fired when the specific interval of the timer elapses. The class that is registered to that event (Bar) within event de-registers the event and sets the reference of the instance to null. This is how I would do it, tested and it works.

public class Foo
{
    public delegate void SelfDestroyer(object sender, EventArgs ea);

    public event SelfDestroyer DestroyMe;

    Timer t;

    public Foo()
    {
        t = new Timer();
        t.Interval = 2000;
        t.Tick += t_Tick;
        t.Start();
    }

    void t_Tick(object sender, EventArgs e)
    {
        OnDestroyMe();
    }

    public void OnDestroyMe()
    {
        SelfDestroyer temp = DestroyMe;
        if (temp != null)
        {
            temp(this, new EventArgs());
        }
    }
}

public class Bar
{
    Foo foo;
    public Bar()
    {
        foo = new Foo();
        foo.DestroyMe += foo_DestroyMe;
    }

    void foo_DestroyMe(object sender, EventArgs ea)
    {
        foo.DestroyMe -= foo_DestroyMe;
        foo = null;
    }
}

And in order to test this, you can set up a button click within a Form, something like this, and check it in the debugger:

Bar bar = null;
private void button2_Click(object sender, EventArgs e)
{
       if(bar==null)
             bar = new Bar();
}

So next time when you click the button, you will be able to see that Bar instance still exists but the Foo instance within it is null although it has been created within the Bar's constructor.