For example, you have a combo box which contains 10 elements including the one that is currently selected. When you prompt to drop down the list to choose another, should the currently selected item also be in this list?
It should be listed. And the default behaviour of browser combox box dropdowns is to have the selected item as first item.
Otherwise, clicking the combo box, it would be unclear how to retain the currently selected value once the drop down has opened. While clicking outside the combo box might reselect or reset to the currently selected value, it is much clearer to have the currently selected value in the combo box listing, preferably as first item, thus allowing to reset to same value by clicking it. This also presents all choices in a clear and consistent way.
Yes, it should remain in the list.
Imagining myself as the user for a moment, when I type something in a combo-box, it helps me select an item from the list below. How will I know that I've typed something that's actually found in the list if as soon as I finish typing it the item no longer appears in the list? Instead, give the me visual feedback by keeping the item in the list and highlighting it.
It may seem redundant to display the same text in both places--which, I assume, was the reason for your question--but the second place it's displayed (highlighted in the list) serves to confirm that the first (in the box) is a valid entry. You might be able to get around this by highlighting the text box once the full query is formed, but it won't give the feedback the user's accustomed to so many users will likely find such a format unintuitive. There's nothing to loose by the slight redundancy, so you might as well leave the entry in the list....just make sure to highlight it.