Having different User-Interface is already answered, except for maybe
So, in a public setting is it possible
to have the program set up to
accomodate both languages at the same
The answer is yes. Different users on the same system can use different UI-languages at the same time. They don’t even have to manually pick the language. If the corresponding language is installed for LibreOffice, it will autoselect it. Only when you run your desktop-environment in a different language, you have to manually set the language options as described in the answer by mariosv.
In case you want to run two copies of LibreOffice as one single user, you have to use different user-profile directories as explained here: How to NOT connect to a running instance
To edit CJK or RTL languages, you need to activate the corresponding checkboxes in Tools|Options → Language Settings → Languages, otherwise the additional formatting options will not be shown. (Just opening/viewing the files works without those options enabled)
To actually translate the document content itself (i.e. the text you write yourself), I’d suggest some other tools such as OmegaT (http://www.omegat.org/en/omegat.html) that can handle the OpenDocument format.