wow, thats bad. I mean my porch/canopy was shit, but thats another level. That "flashing" is basically a scam, im not sure what advice you need but at the very least that flashing needs sorting out.
My builder used offcuts of an old fence (i had stored for burning) in my porch roof and cut the canopy rafters too short so added bits on the end. As its exposed it looks crap and i'll have to box it in with soffit board or something. "Most people make a feature out of the exposed timbers" he said. At that stage i just wanted them gone so i let it go, another job i need to finish.