1. I think if you catch them in a cage trap, you can build the cage and designate their items for dumping.
2. If you designate a dumping zone next to a cliff, they will throw it off, however, it will not disappear from the map (unless it falls into magma and is destroyed). Magma-safe materials will only be destroyed int his fashion by falling into the magma sea.
3. There are other animals which can be trained, but certainly not all of them. Here's a list.
http://df.magmawiki.com/index.php/Kennels4.No, but if a bridge is lowered onto a sufficiently large creature, the bridge will break instead of atom smashing it.
5. Not that I'm aware of. even if it is made pet impassable, they can still go through when a dwarf opens it. The only way to fully prevent animals going through is to restrict use of that door all together.
6. Did you designate the zone as a hospital? Do you have a "chief medical dwarf" noble? Do you have the proper furniture in the room? You need beds for the patients to rest. You need containers as well to hold supplies (though, this is bugged right now). Having tables next to the beds will let operations be performed on them so less blood gets on the floor. Traction benches next to the beds allow your doctors to do work on bones. Having casts and splints is also important for bone work. You need soap to clean infections, but there are bugs related to soap currently, so you may get some cleaning errors to deal with. Thread is needed to sew up wounds.
7. Not yet.
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