I'm working with background tasks.
If I press the home button once the app will call DidEnterBackground and I can run anything here - Ok
If I press the home button twice and swipe the application out of the screen, finalizing it, WillTerminate will be called and after that, the app DIED, I can't do anything more.
On the Android I can do it and keep the app running, without show it on the android's app switcher. There's a way to do it?
And how I re-open the app every time I kill the app (Every time WillTerminate is called).
You cannot avoid the kill by the user. Apple philosophy is that the user is the "commander-in-chief" and he can decide to kill your app when he wants (and the kill must be real, no hidden processes). All background tasks of the app will terminate with it and you cannot reverse the user decision (i.e. restarting automatically).
I don't see simple solution for your problem. The only thing that I can think is to put a big alert message to the user, when a specific task begins, saying:
"don't kill this app from the switcher while this operation is running ..."
or, save the state of the background process and restart it at the next run of the app.