Does anyone know of any good and easy-to-play tune or song with all dominant 7 chords? I am practising the dominant 7 chord shapes and was thinking that it would be nicer if I am not just randomly playing the chords but a tune that I could enjoy along with.
Try finding some blues songs. Every single one of them contains dominant chord progressions, for example Hoochie Coochie Man or if your looking for something more jazzy try Now's The Time from Charlie Parker
You're not going to find many songs with all dominant 7ths - the main reason people use them is the way they lead into a major chord. They add movement and interest to a progresion. Likewise there's little point just practicing the shapes alone because you'll rarely use them that way, most of the time they're used as a substitution for a major chord in a bog-standard progression. Pretty much anything by The Beatles will give you some good examples of how to use them, Hey Jude's a good one, or simply choose a song you know and experiment with subbing in 7ths and see how they affect the sound, they might sound great or they might sound wrong - it all depends on what else is going on in the song.