Anyone know what this type of wall is called? And how I should fix it?
Hmmm. Looks like insulated plasterboard? Not sure I'd hang anything on that unless the fixing went back in to the solid wall behind it. To fix it I guess you'd fill the hole then plaster.
If you must put the rail back on, the idea of running a wooden support up and down to spread the load is a good one. That's assuming you can't drill all the way through to whatever is solid behind it, which would be the best way I suspect.
Hmmm. Looks like insulated plasterboard? Not sure I'd hang anything on that unless the fixing went back in to the solid wall behind it. To fix it I guess you'd fill the hole then plaster.
If you must put the rail back on, the idea of running a wooden support up and down to spread the load is a good one. That's assuming you can't drill all the way through to whatever is solid behind it, which would be the best way I suspect.