In v6, once your Tama reaches the teen phase, it will no longer be satisfied with normal baby food or baby milk. You'll have to go shopping for something more filling for the little fellow. Your money will be tight until your Tama reaches adulthood and can go for a part-time job, so watch your spending. Sometimes, that weird black Tama with the hat will ring your doorbell and give you 2000 Gotchi points (I think he does this daily so you can eat...), so don't panic if your funds run low.
As for your CD on the Music Star site, you earn Producer and CD exp. as you play the mini games. Just remember to equip your CD of choice as your main one in the status screen.