"Dry ridge" is just about standard now on new build, Ferlew. To do this effectively, all the ridge tiles would have to be taken off and re-fixed with the new system Simply put, it's a matter of restraining the ridges with metal or plastic ties fixed to the roof timbers.
My own preference for existing situations like yours is to drill a hole in each end of the tile... screw a piece of galvanised fencing wire to the ridge board (timber).......... pass this up through the hole in the tile, then bend it back down to the ridge, and hold with another screw.
Do this at each end of the tile. Fencing wire can easily be bent into a small circle to accept a screw.
With ordinary mortar, point up the junction of the tile to the slates/concrete tiles......... and point up the vertical joints between each tile.
It's not usual to "solid bed" these days (underside of tile completely filled with mortar.
They'll never come off again.
Yes, best not to dwell on the state of many of our older roofs.... and don't even think about some of the chimney stacks !!