Could this also be used in the sense of eating and drinking? For example, in a hospital- "he doesn't take food or water"?, ie he does not eat or drink?
No. The word for "take" in that sense is "assumere", but it is not so common with this meaning.
It can be used, for example, in hospital, to say somebody takes only liquid food "Assume solo liquidi"
That word means hire as well. ;)