How do I move onto round 2, 3 and 4?

To move onto round 2, 3 and 4 you need to have collected all of the socks required to complete level 100 and you also need to have collected 1 of every set of socks. If you have completed level 100 without collecting all sets of socks you will be in ‘Open Play’.  There is also an Open Play at the end of Level 55 to allow you to catch up with sock collection and gain any achievements you have missed.