looks like a bad attempt at a join one side looks like fiber cement slate the other tiles they have taken the tiles over the fiber slate by six or seven inchs and just blocked it off with mortar.
depends on what you was wanting done may surprise you or you could keep the cost to coat the roof and re-tile next year but for sake of 1200 or so more you getting a new roof that lasts for 30 or so years instead of a few years
u can either measure down from each top corner down onto the main roof or when u sit the tile in the position take a piece of tile batten and lie it up the roof against the tile this will let you mark the angle on the tile u can then use that line as a guide
The slate will have to be re-dressed and then re sized once they have been taken off you will also aim to get one side out of the two sides so your gona be at least short of slate for one side
ive 20 years in the trade m8 and its rains here 310 days of the year the fittings for cast to plastic aint suited for here you either butt two stopends together and cover in lead or give a mega overlap