I had a broody hatch 3 chicks. They, and mama, are in a cage inside the coop. They are 7 days old. How do I go about letting them around my 6 other hens? I cant keep them in the cage forever! Will mama protect them? The other girls have seen them since day 1 of course, inside the cage. Im scared! 

It is so hard not to worry! But everything I have heard or read says earlier introduction is better. I had my first broody hatch earlier this year and waited a bit too long before the introduction (babies were three weeks). It still went ok, but next time I will try introducing them much earlier. I think at one week they will be moving well and of course they will have momma for guidance and protection. Pick a time and day you can supervise, then go for it! And let us know how it goes.
BUT the babies never took any harm or injury even with a cowardly mother. The big girls quickly lost interest in the littles and the littles learned not to get to close to the bigs. Everything worked out fine. 

