Here is my take on the OS
This is where all your apps/games are. It is all mixed up, I assume the order is of whats recently used. Each app/game icon allows you to see trophies, shared media, news feed (leaderboards announcements, friends activity), DLC without the need to start a game. Of course you start the app/game on the tab too. Note the first orange icon, is always first on the list, it is the home screen which I will explain in the second screen. Finally the above icons are PSN Store, announcements (can also be shortcut, for example you get game invite, click on announcement to go to game), friendslist (messaging, view friends profiles, friends activity, who's online and etc), your profile, and finally settings icon.
This is the home screen. You get to this from the first orange icon on the first screenshot, this icon is always first on the app/games list. The homescreen is a clusterfuck of random shit, adverts, whats trending, what your friends did, recommendations, whats new and etc. The feed is bigger than it appears, you can scroll down for more.
This is self explanatory. You get to this from friends icon or notification tab at the top. seems to be a group chat.
Again self explanatory, you view this from shared media part of a game icon, or from homescreen of random shit if its trending or new, or your friends profile or activity feed. You can fullscreen, start/resume game or like video.
Here is a livestream. It seems you can comment of live stream your viewing as well as the livestreamer has the option to broadcast themselves with a camera as well as voiceover. Of course this is also viewable on a phone. Note I am not going to bother going through all the phone screenshits. But it seems you can do almost everthing on a tablet, smartphone, excluding actually playing games (messaging, PSN Store, watching shared videos, activity feed, viewing friends profiles and etc).
My overall impressions based on screenshots, looks functional but looks bland as fuck (I am guessing you can change backgrounds though). Of course you can multitask between all of this.