The third picture seems to show the shingling job directing water right to the base of the chimney chase (the wooden chimney enclosure.) There's no sign of any flashing in the picture, but there may be some. In any case, something must be done to divert water away from this area. Any sort of repair would be short lived with water continuing to pour into this intersection between roof and chase. Never should have been roofed this way in the first place.

coody:

With the exception of the obvious tree branch sticking through the roof, diagnosing roof leaks requires years of experience.

My neighbor was sure his roof was leaking. In fact, the flue gas in his metal chimney was condensing and dripping.

Call a professional with an excellent reputation. This isn't a DIY.