In natural languages that morphologically mark animacy vs. inanimacy on a largely semantic basis, (e.g. "hamster" is animate, "stone" is inanimate), which of the two noun-classes do terms for the following categories typically fall into? a) terms for dead organisms, and b) terms for parts of organisms that don't live independently of the whole, e.g. "fingers"?
At first, some important remarks on animacy.
Animacy is more like a continuum, meaning that it doesn't behave like a dichotomy (animate or inanimate) but rather "a more or less continuous category ranging from most animate to least animate" (Croft 2003: 130), cf. Dixon's animacy hierarchy, human < animate < inanimate. This is semantic animacy or what Croft calls "animacy proper." Obviously, it is language-specific. For example, trees are inanimate in Slavic languages whereas they are animate in Algonquian languages (Plungian 2011: 142, n.47).
Interesting examples from Russian:
trup 'a dead body' [inanimate]
pokojnik or mertvets 'a dead person' [animate] (from Plungian)
A Wikipedia article on animacy (its Russian version) aslo mentions cases when the same noun can be both animate and inanimate (with no difference in meaning), e.g. virus 'virus' or robot 'robot'.
Some examples from Dyirbal (Dixon 1972)
non-human animates: some birds, moon, storms, rainbow, boomerangs, some spears, etc.
Now, to make things more complicated, this semantic animacy interacts with many other things, like definiteness, referentiality etc. (the extended animacy hierarchy). See Croft for further discussion
By pure coincidence I happened to try this out before I saw your question a few hours ago here in Georgia.
In Georgian nouns are not marked for animacy, but some verbs are.
"To have" is აქვს akvs for inanimate nouns but ყავს qavs for animate nouns.
I was joking around with my Georgian friends and tried to say "I have one head", just to test this out in fact.
მე მყავს ერთი თავი. animate
But my friends corrected and taught me that I should say instead:
მე მაქვს ერთი თავი. inanimate
So people are animate in Georgian, but body parts are not.
(Side note: Cars are the only nonliving things in Georgian which take the animate word for to have.)