Every sentence has two things: a subject and a predicate (verb). When you are asked to give the predicate of a sentence, they probably want the complex predicate. If they ask for the simple...
No. Every sentence does not have a simple predicate. Some sentences are only an an exclamation. Ouch! Some are only a verb. Stop! Some have a subject and a verb. Jane left. And some have a complex...
In the sentence "was" is the auxiliary verb and the simple predicate and 'was surprised' is the compound verb (helping verb 'was' and the main verb 'surprised') and the complete predicate.