1) I don't think they do. Someone else might know otherwise. I think it's all or nothing each strike rather than cumulative HP damage, subject to attack skill rolls and physics.
1a) I used DFHack and ran "gui/gm-editor" on a unit and checked under "body". The only useful number I found is "blood_count", which tells you how far a living body is from bleeding to death. There's a list of wounds stored with who caused them and what's wrong with the part, but no numbers.
1b) First is material. Bronze colossus flesh is much stronger than a forgotten beast made of water (which will die in one hit to anything.) The wiki says that the strength and toughness attributes make you slightly more resistant to damage, while recuperation helps your wounds heal faster. Body size is very important to damage resistance. The amount of blood a living creature has depends on body size. I think one of the physical attributes (toughness?) has an effect on blood capacity, if I recall correctly.
1c) It depends on the weapon and who's using it. A giant with a steel axe is going to chop off limbs easily. A kobold with a steel dagger is going to have a difficult time without a lucky strike to the heart.
2) Has blood remaining, hasn't suffocated, brain attached to body and not injured, lower body attached to upper body, and upper body exists (not being smashed under a bridge, frozen, obsidianized, or dropped into an eerie glowing pit.) I think doing enough damage to the upper body might also kill (mangling.) Suffocation can be caused by drowning or damaged/paralyzed lungs/spine. Hunger or thirst can kill if the creature requires them. Same with old age.
2a) Head, lower body, or upper body.
3) Lower body attached to upper body, and upper body exists and is not mangled. Special case for undead hands with no upper body: Has ability to grasp (for example, hold a weapon.)
3a) Upper body or lower body, except undead hands, which would mean loss of the hand or all fingers (if it needs them to grasp, unlike crab pincers.) I think separating the hand from the upper arm or lower arm might also "kill" the hand until it is reanimated again without the part. (This might have been changed at some point, however.)
3b) The main part of the body for every creature is usually the upper body. (Ghosts are listed as missing the upper body as their only wound, which means they have no body.) For undead hands, it's the highest part still attached (upper arm, lower arm, or hand.)
3c) The part benefits from the original creature's stats, as well as a supernatural boost to strength (original*1.3 + 1000) and toughness (original*3 + 1000) attributes.