I want to move the selector (3 cells selected in the example below) with arrow keys. It is possible to move with one cell selected, can I do it with more than one cells? Thanks. Note: I don't want to move or copy contents of the cells. I just want to move the selector (big rectangular box) as easy as moving a single cell selector. (The question in the link is not answered yet either, and the offered solutions what I was not looking for).
Based on the above image: If you mean moving selection of C3:C5 to become D3:D5, then it is possible in somewhat cumbersome way as shown in Bandersnatch's comment.
Moving N cells right [left]: (follow either normal text or text in [brackets])
Highlight a cell in leftmost [rightmost] column of selection using Tab or Shift+Tab if not already done.
Press Shift+→ [Shift+←] N times.
Press Shift+Tab [Tab] once.
Press Shift+→ [Shift+←] N times again.
Moving N cells down [up]: (follow either normal text or text in [brackets]
Highlight a cell in top [bottom] row of selection using Enter or Shift+Enter if not already done.
Press Shift+↓ [Shift+↑] N times.
Press Shift+Enter [Enter] once.
Press Shift+↓ [Shift+↑] N times again.