Don't worry first -kitties don't die or run away because of lack of food. The food you need is the same adult kitties have. The kibble you find at kittycats mainstore. The different flavours only reflect the number of bowls in each pack.
You won't need milk since they're under 7 days old. After they start gaining love you have a choice: milk or 30 minutes of cuddles so they get to 100% love in a week, or wait 10 days.
About making your sick kitty better: it just needs food. There will be 7 days of recovery period (even after he or she's not hungry anymore -they need 7 days to recover. You can check how much time remains by clicking on the kitty and looking at the information in local chat). You can also get a get well drink from the mainstore and the kitty will be well immediately, but just with food they will get well on their own in a week.
I hope this helps