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Try to press Alt-R and then try to select with keyboard (no mouse) the folder you want. Every time, some folder in the combobox is selected, the combobox is closed and the folder is immediately applied. So the combobox is more or less unusable with a keyboard, just with mouse. Folder should be applied when Enter is hit.
You can access recent folders using the up/down arrow keys, no need to select the combobox.
Sure, you can. But when you have 20 items in the combobox, from which some are expensive to load (like NetBeans repositories root), it losts usability and I end up expanding combobox too see more - eight; items at once.
Unfortunately not easy to fix; generally considered to be a bug in Swing. (Visible many other places, e.g. dropdowns in project Properties dialogs.) There is a client property which seems to work (at least for navigation using Up/Down, not Page Up/Down); tested on Ocean, GTK, XP. release65/contrib #fc48f717a565