I can confirm the issue of unexpected behaviour of function keys in Google Spreadsheets using Opera 19 and 20. Looks to me that a recent change in GDocs broke it. Chrome, Firefox and Internet Explorer all work fine though.
Broken function keys include cursor keys, tab, delete, backspace and F2. But only in some cases: Cursor keys, delete and backspace do work inside a cell (but not when I enter by double clicking) but can't move/empty the active cell.