Translation:The dog likes you because you have food.
Yes, but you'd have to change the word order: Du har mat, därför tycker hunden om dig.
därför att is a subjunction (which joins a clause and a subclause) but därför is just an adverb that can be used to join clauses, therefore both clauses are main clauses and will use the V2 rule.
Not quite. "Feed", when used to mean giving an animal sustenance, is generally reserved for animals bred for commercial/practical purposes. I might give my beef cattle "feed", but I'd give my cat "food"; I might give my hens "feed", but I'd give my pet mouse "food". I would never say I give my dog "feed" unless I was fattening him to be part of a good Chinese meal!