I think "He's always wanted to make her food" should be accepted.
Correct, because "has" is an auxiliary verb here. Report it.
How can I find back to this question and report button now?
Would 'har villet å lage' be grammatically OK too?
No, because 'å ville' is a modal verb.
For me this would be: "She rarely cook for him, because he always does". Poor man that can't cook the are just lazy. I cook for 35 years and it is not my job.