"He cooks the food."
Translation:Lui cucina il cibo.
Both "Cucina il cibo" and "Lui cucina il cibo" are correct translations. They mean the same thing.
Italians would be more likely to use "Cucina il cibo" unless the context of the conversation is not enough to tell you that the omitted pronoun is lui. In natural everyday Italian pronouns are ONLY included when the subject is unclear from context OR if you want to add extra emphasis to the subject of the sentence.
'cucina' is not feminine - it is a verb, and verbs don't care about gender (he cooks, she cooks, either way we say 'cooks'). Regular verb conjugations follow a nice pattern (irregular verbs like 'essere' are a little trickier). Good table here: http://italian.about.com/library/fare/blverbs01.htm
'Cucinare' means 'to cook', so it conjugates as: io cucino (I cook); tu cucini (you cook); lui/lei cucina (he/she cooks); etc.