pwFoo as far as I know you can't have push notifications without third-party servers. You need at last Google and/or Apple service. Or a more generalized third-party service like used above.
If you know how to implement the push notifications, you could have a try at creating the extension yourself.
I understand if you're not interested in a premium extension. If you need very few features, you could maybe describe in more details what you're looking for? If by embed you mens third-party services, you could use imgur and the media embed extension to paste imgur albums in the post.
