Can you always use må instead of trenger? - 'Huset må har et nytt kjøkken'
"Huset må ha* et nytt kjøkken"
That would be closer to "The house must have a new kitchen".
Would a native speaker find it weird if I use 'behøver' here (despite of being formal, of course)?
I've been living in Norway since 2003 and I can't recall having heard "behøver". They use "trenger". "behöver" would be perfect in Swedish.
Why is it "et nytt" and not "en ny" ? Does the adjective shouldn't go with "kjøkken " ?
"Et kjøkken" is a neuter noun, so the adjective "nytt" does agree with it.