1. There is no one-click solution to start playing random tracks, unfortunately. The only way I know of is either creating a root playlist of all your songs and shuffling, then playing, that, or using the database and selecting artists, then all tracks, then any track, and making sure shuffle is on (and repeat mode set to shuffle if you want it to continue playing and reshuffling forever).
2. That's the count of how many tracks are left to be loaded into the playlist. If you have a lot of tracks to load (say your entire library of several thousand), you'll see the countdown as it's creating the playlist.