How to repair interior ceiling . .

Hi All,

Thinking of rehabbing an Eichler style home. This may not be a true Eichler, but has many elements that are Eichler. The ceilings of this home are not paneled with wood, but some kind of inter locking foam board. I've looked at two homes, both only 2 blocks apart. Both have these kind of ceilings. The home I'm looking at has had lots of leaks and these ceiling panels have been patched (rather crudely I might add.) But most of these panels are sagging.

What I want to know is what are these panels made of (they're about 12 to 16 wide running perpendicular to the beams. Not sure how much work is involved in fixing them?

Also wanted to know how thick the roof boards are under these panels?

There is a lot of dry rot on the roof panels near the eves and rafter tails. Are these hard to repair? What would be a ballpark estimate?

Thanks!

Scott