As of now, it seems to be ongoing. But keep in mind that the publication schedule might be irregular and subject to various factors like the author's creativity and publishing plans.
As of now, the Classroom of the Elite light novel is indeed still in progress. The author is continuing to build the world and develop the characters with each new installment.
The Haruhi Suzumiya light novel isn't ongoing. The story reached its completion some time ago. But you can still enjoy the existing volumes for a great read.
Not sure about that. Maybe check with publishers or scan through some fan discussions online. That could give you a clear answer if the 'Extra Remake' light novel is still ongoing.