WA 1977 Built house added-on room water leaking

There a foam biscuit with various outer layers used for various purposes incl cool-rooms.

What you have there is equivalent to what they use for solid caravan annexes, the bottom surface in the pic there is probably thin ply, whats likely on the other outer side under the roof sheets is thin sheet metal usually painted fridge white, with c-channel around the edge, between two sheets looks like a H after being joined with silicon and rivets. Basically you could remove the roof sheets and still have a usable roof however its now covered in tek screw holes.

Actually that stuf around the bottom under the windows is poss the same stuff but a dif ply

 

Actually hindsight I'd say those roof sheets are prob glued straight onto the foam, the glues prob deteriorated so not difficult to separate/remove and replace with some new sheets, or as said earlier your could lay some batons across then re-sheet with trimdek, this would also lift the height, possibly allow you to slide the top end up under the lower lip of the tiles for runoff.

If your not good with DIY get a few ideas/quotes from Handymen
I personally prefer the quality of trimdek from Stratco vs bunnings

 

Looking at those downpipes they discharge to ground next to the walls of the sunroom. Water would pour out and then run along the slab and under the seal to the room.

Divert the downpipe discharge for a starter, and then dig out and run new silicon beading outside to seal it and see how it goes.

 

This will be toxic should it ever burn.

 

Lots of toxic products in these old homes authorities don't like to talk about including asbestos, look what happened to James Hardy and victims, imagine the costs to replace it all.