BetterRed,
theducks - thank you for your response.
I forgot, but now tried: changed UI language to english. Language tasks work well, assign to hungarian or to english, too, autocomplete too. So the probleme is, only, when the UI language is hungarian. So...
Changing UI language to russian: assign by dragging does not work for ANY language. But autocomplete works, with russian too. But, in this case may have importance a character set, too - russian's is cyrillic, while my computer uses (wrong called...) "latin" letters. So...
Trying italian: same, as with russian.
Trying again, with hungarian, more deeply: same, as russian - no one language assign works! Except of "latin". And, in the list of used languages this is the only one, what is same in english and hungarian: "latin". All others are different (magyar - hungarian, angol - english, orosz - russian, and so on).
So, the error is in the internal solution of localization. (Not in translation, simply!)
About autocomplete only, in languages field: I set completion_mode to "contains". If set it back, to default "prefix" - autocomplete works! But, first, it is not a solution, because this parameter better to be "contains"; second: in russian autocompleting works well at completion_mode = 'contains', too.
Total confusing with autocompleting... 
May I ask you, to try in your Calibre, to change language to Hungarian and some others, and check the phenomen, written above?
At me: Win7×64, nearly last Java (8.51). (Calibre uses Java, does not it?)