Suspending means that its memory was preserved, so the app doesn't have to do anything !!!

While suspending may be the first state, the OS can choose to fully evict the app from memory if it needs it for other tasks. So a "good app" saves state before being suspended so that upon resume, it can restore from disk even if it was "killed".

Yes, but in practice almost all apps don't do it always with the complete state,; and on phones that don't kill them so easily most of the times you can switch between apps without problems.