It is normal behaviour for the parents to move their young from place to place until they are free swimming. They will then guard the young for a period of time.

You need to raise some baby brine shrimp or something as a first food or they will indeed starve.

Parents may be more likely to eat after they become free swimming.

You may want to transfer them to a separate tank with no parents or other fish to raise them.

Many sources for angel breeding out there.....Young will grow fast........

Library or book store, or the web is a good place to start.

Congrats and good luck.