You dont need a wifi connection to play songs download (from the service) to your device. The only time you would need to connect to wifi is if you want to update your stations.

As for picking a specific song, no you cant use the free service to play the song on demand, however if you own the song (more less what the premium service is) and transfer it to the player, than it works like a normal MP3 player and you can play whenever you want. What ive found thou' is that the reason i started using the service (and player) is because i didn't like listening to the same things over and over again. You could always place the artist into a station and hear the song indirectly, and if you "heart" it, it will play more often.