Yes. Óleo = oil / Olive oil = azeite

On these type of questions, hovering over the word won't show you the answer. That would defeat the purpose of the exercise, which is designed to make you remember the words. You can only see the answer when hovering when the word is new or highlighted/underlined in blue.

{Gostar} is always followed with {de}, just like {precisar}. It's just a rule, and there are a few other verbs like that. I have forgotten the formal term for words like these, perhaps a native speaker can expound on that.

{Da} primarily means "of the" or "from the." There really would be no proper use for those in this sentence. Even though {da} can also mean "in," there would be no place for the word because "de" would already be in use. It wouldn't be proper to say "Ela gosta de da salad com azeite" as if to say, "She likes, in the salad, oil." Hope this helps.

If the sentence would be: 'She likes THE salad', then 'da salada' would be correct.