Gallery: Motos usually come with Google Photos as the gallery app. It's labeled Photos in the app drawer.
App drawer: Recent Android phones default to gesture navigation, quickly swipe up from the bottom of the screen to open the app drawer. If you want the buttons back go to Settings > System > Gestures > System navigation and select 3-button navigation.
Re: Nova, Nova Prime and Nova 7. Is this the Nova Launcher? When you restore a launcher backup the icons for apps that don't exist on the new phone are grayed out on the home screen. The LG Contacts and Phone apps are not on your Moto phone You need to replaced the grayed out apps with the Moto equivalents from the app drawer.
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