I heard Norwegians don't use "elsker" very often, and it is much stronger than "love". I noticed though on duolingo it's used almost as often as "liker" and for trivial things such as the one in this sentence.
It's much stronger when said to people. The rest of the time it means roughly the same.
The audio is a bit confusing — it sounded like "vi elsker bygda", without "de"
It's all about context. Before an adjective, "de" means either "the" or "those," but before a verb, it means "they."
It's a feminine noun, so if you're in the habit of using the definite form, 'bygda,' you should go with 'ei bygd'.
I got it wrong and it said that "bygda" means "the hamlet". I've never heard that word used for anything other than the play.