Do App branding plugins allow push notifications?

I'm using Membership on my multisite to start a serial fiction (by subscription) site. I had looked into services like Mobile by Conduit for branding an app. I'm interested to know a few things about you Droid and iOS app creation plugins: 1.) do they enable push notifications 2.) will you guys help me figure out a way for users to download content to device so they don't have to remain online to read? (I would love to include an in-app epub reader, but that might be too much to ask.) 3.) I'm assuming the same membership rules will apply within the app as on the website?

Thanks!