IDLE and Python/tkinter have nothing to do with the handling of keystrokes and their direct interpretation.  The behavior you describe, the Ctrl key being disabled in Ukranian mode, strikes me as a bug in either Windows or the Input Method you use, or, less likely, the tcl tk GUI framework.  Someone who uses the Japanese IME with IDLE thinks Ctrl continues to work right in Japanese mode, but will check and report to me.

IDLE offers menu entries for most shortcuts.  Indeed, shortcuts are shortcuts relative to using the menu.  Cut, copy, and paste are on the Edit menu.  It should be accessible with Alt shortcuts.  C, C, and P are also on the right-click context menu.