Disagree. Either a or the make perfect sense and are grammatically fine in english.
Could be the nasty neighbors '... they usually live in a forest' (given their lousy behaviour - for example) - it generalises their likely place of residence, or bears '... in the forest', it specifies their place of residence.
Well, no, but yes as well. "Elää" is "to live, to be alive" in a more general sense while "asua" is more like "to live, to dwell" in a house or an apartment but also in a nest etc. So you can use both for people as well as animals. But when talking about living conditions, you are much more likely to use "asua" for people and "elää" for animals.