How to map such stairs?
Is highway=ladder suitable? How can I specify that this is a fire stairs?
imho highway=ladder is applicable, for the other property, no idea. There is a whole emergency space in the tags.
emergency as a key is used both, to define a feature (or property) or as an access restriction 
Most used value I found for your case is emergency=rescue_ladder | Tags | OpenStreetMap Taginfo
but possibly I missed something.
There are also uses of emergency as a prefix, you could use emergency:highway=ladder (not sure if I would do it)
is it forbidden to use these, or are people sometimes using them to get on the roof (is the roof generally used?)
Getting inspired Node: 12613492307 | OpenStreetMap
I think I’ll tag them as
emergency=rescue_ladder
support=wall_mount
highway=ladder
I think highway=ladder is suitable, because the wiki has the following similar examples::
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