You could use Klucel and SC6000 (It will do no harm) but this is not "real" leather so there is no strength in it and it will break because of poor ingredients eventually no matter what. It cannot get red rot. PVA works pretty well to repair this sort of crack but ultimately the cover will need to be replaced.
The flappy "white strip" is part of the text-spine liner for this book. Mull is simply one type of liner for the text-spine of a book that extends outward on each side in order to be glued to the boards.
If you are not making a new cover, I would Re-case the book because opening it up / separating the two parts will facilitate strengthening the cover cracks from the inside. Just make sure the text will fit back in the cover! It is possible that you don't have to break the hinge that is unbroken but you can peel back the paste-down to work on the spines.