Sometimes it is easier to remove the featheredge as if you counter batten and batten then you need to increase the height of the facia boards, and can also interfere with the junction with any other roofs or window details.
You should remove the first 2 courses of tiles and fix the lead to a batten at least 100mm above the porch roof and then replace the the 2 vertical courses.
Its not a huge job but due to the height of the building you would need a scaffold front and back which would be about 6 to 700 pound. The work would be about another £850
They are not fitted correctly. Each course of tiles should cut into a bonnet hip. In the picture the bonnets are sitting on the tiles that should be cut into them.
The type of underlay you have should not extend past the slates. There should be underlay support trays fitted which overhang the facia and provide the drip into the gutter.
If you cut the membrane back it is possible although unlikely that some water could come of the slates and blow back...
The leadwork and cement work is very poor.
The fact that you were able to take close up pictures suggests that the roofer should have little trouble carrying out a proper inspection.
I would think that most quotes would be in the region of £2000.
Acrypol is a temporary repair solution that you paint over the entire gutter,
you could use lead sealant in the cracks as a temporary measure.
if you want the window to be square with the tiles then you simply put the bottom trimmer in level with the tilling batten.
Usually I cut the rafter directly over a tile batten and fix the trimmer there.
The bog gutter should have a flat sole of approx. 150mm an upstamd up the brickworkof 100 mm minimum and cover flashing chased into a brick course. On the roof side it should extend a minimum 0f 250mm up the roof slope on a ply board and the tiles are replaced ending aprox 75mm up from the...