What do you mean by 'open tasks'? If you mean tasks he has been assigned, but not yet completed, you can say Ruslan has yet to complete his (assigned) tasks. Does this suggest they are overdue? Not really, but it would depend on the context within which the statement is made.

I would answer yes to both of your questions, it is correct and it does imply lateness. If the sentence read: “Ruslan has open tasks” it would not imply being late.

Ruslan hasn't finished his tasks. Ruslan hasn't finished his daily/weekly/monthly tasks. Is the natural colloquial way to say it. Or you are better saying "assigned tasks" it is a little odd to use open and tasks together

What tasks do I have?!😅

1. Yes it is correct. 2. Let me give you another example: We have made progress, but of course! we have not yet reached the end of the road; we are a long way from achieving our objective. In essence, the open tasks have not been finished, so he has to finish them.