Can I install downloaded app even if it's not available on the App Store I have few app that was downloaded to my Mac, now there are not available on the iOS App Store anymore, so can I install them when I get a new phone even those app are not available on the App Store?
Yes. You can synchronise them by connecting your iPhone to iTunes on your Mac. It will synchronise all the apps that are in your iTunes library with your new iPhone.

That's why it's handy to download apps in iTunes as well. Also updates and keeping older versions from the app around. So you can go back to an older version when there is a bug introduced in the newer version.