This is something you can decide yourself in the model, since a microflow decides when you send a pushnotification.
I did some reading up. On the Apple side this is in the design and not something Mendix can change. See stackoverflow: http://stackoverflow.com/questions/14872088/get-push-notification-while-app-in-foreground-ios
Which one? I use the provided Java action 'SendMessageToUser', but this does not end up in the device message que but is catched by the app itself when the user is actively using the app.