Position-jugdment problems simulating actual play I'm interested in collections of chess problems 
where we are not told beforehand what is happening in the positions presented, 
but we have to decide by ourselves, whether something clear exists (a winning or drawing combination, a good move or plan that keeps the initiative) or whether the position presented is still unclear. Clearly the goal is to exercise analysis, intuition and general judgment of positions, by simulating actual play.
So are there collections of problems of this type, in print or online?
You can find such positions in Dvoretsky's books.  Also, in "The Defense Triumphs" by Kotov. But in general I am not aware of a collection of positions without a clear objective presented.

Then there are a couple newer "positions you must know" books that you might explore.

Of course if you go over annotated GM games as if you are playing the game, thinking before reading the next more or comments -- this is a good way to achieve such training.