1) How long can it take for longterm symptoms of a forgotten beast syndrome to show up? Is is possible for a dwarf to carry a syndrome for ten years or more before experiencing symptoms?
Not totally sure-- but no, it's not that the syndrome is latent for ten years. It's that something is spreading it, something you can't find.
2) Can a dwarf catch the syndrome by handling the corpse of a victim of the disease? how about walking through his blood?
No. Contaminants do not spread from picking up an item. And there's no way for the deceased's blood to carry a syndrome, although it is possible for the original creature's blood to carry the syndrome.
3) Are there any indications that a dwarf is carrying a syndrome even if he is not showing symptoms?
It's not the dwarf that carries it; it's the contaminants. Look on inventory. Look for forgotten beast blood or extract on the feet.
4) Can items carry the syndrome and pass it on to a dwarf that handles it?
Not to dwarves that handle it. But items that are contaminated will pass their contaminants to the floor when they get wet, and then walking over that floor can lead to dwarven infection.
5) Any other advice for dealing with syndromes?
I can't figure out whether shoes and such protect-- sometimes it seems they do, other times, it seems they don't. Making all members of your fort military with compulsory footwear might help.
It can be really really hard to locate the stuff. Look through your deceased forgotten beasts and/or clowns for one with deadly blood or noxious secretions or deadly dust. That can help give you an idea where it all started.
Make a dwarven bathtub (trench with 2/7 water) that dwarves pass through regularly. This will help contain the spread. Examine your trench on a regular basis for suspicious blood or extract.
Turn cleaning on for all dwarves.
Make a safe spot for dwarves that won't wear footwear (children, for example). Restrict them to that burrow.
Try and find contaminated items. When a dwarf bleeds to death, inspect the dwarf and his footwear immediately. Dump the footwear if it's contaminated.
Inspect the outside and any muddy tiles (including caverns) carefully. Dwarves will never clean these tiles. You can clean them by building a floor.
Look next to your water source. Contaminants congregate near water sources as dwarves wash themselves clean.
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