How can I make the eventhandler SelectedIndexChance (from a ListView) public in a selfmade UserControl ?

Add a method  to your control class add populate it by this line of code
public  void SelectedElementChanged()
{
      listView1.SelectedIndexChanged +=new EventHandler(listView1_SelectedIndexChanged);
}
/* I set it protected to be only visible by the derived classes you can set it public or internal if you want */
protected void listView1_SelectedIndexChanged(Object sender, EventArgs e)
{
   //Put your code here to perform your tasks
}
When the intellisense appears SelectedElementChanged will appear as one of the control 's method