Redland delta tiles originally would have used purposed made reforms, you may still find some through a decent roofing merchant they were made from Aluminum
Raise the gutter up its too low.
fwiw the slates can be removed and replaced without mastic or tingles.
I'm surprised none of the roofers would know that.
As already said , ponding isn't a leak it's just a pool of water on a reliable waterproof membrane. Sarna is pretty good.
You need to get an approved single ply roofing specialist to take a close look
Good , the verge has to come down . The tile bond is all wrong ,
Something is moving out as the tiles are spreading. That's not caused by tiles slipping .