The simple predicate is always the verb or verbs. Helping verbs are included in the simple predicate, too.
Some of our most common verbs are am, is, are, was, were, have, had, has, can, could, might, may.
Other verbs show action like make, live, run, fly, drink, type, study, think.
The simple predicate in your first sentence is have destroyed. The main verb is destroyed and its helping verb is have.
If you post what you think are the simple predicates in the rest of the sentences, we'll be glad to check them for you.