Is there a reason "he cooks for me" is deemed wrong ?
No, just that the creators didn't add all possibilities. If you see it again, report it.
He's cooking on my behalf...
= anapika kwa niaba yangu. "He's cooking for me" just means "he's making a meal for me (to eat)"
Why is there an ni after the he present tense? Shouldnt it just be anapikia
break the affixes down: a-na-ni-pikia = subject-present tense-object-conjugated verb