TN Mama

First, you should know I've had birds most of my life - parakeets, a Lorrie, and two Cockatiels (one is still living at 25 years old). I've always be fascinated with African Greys. A friend of mine was looking to place her 13 year old grey into a new home because they were just not home often enough to give her the attention she needed. I took Scarlet in 3 weeks ago, and at that time the owner said that she had been molting and pulled all the feathers from her chest. Her chest was bare skin but she began getting a little fluff within the first week and is still getting more fluff. I think she is really happy with us because she started repeating some of our words within a week. Until today, I've been uncertain as to if Scarlet is male or female because she had never been tested. However, she laid an egg today so she is a SHE after all. So what am I to do with that? Does this mean she is happy an healthy here with us? Additionally, the previous owner had not had Scarlet out of the cage in 12 years - very, very sad but she does have an enormous cage 3'W x 2'D x 5.5'H not including the gutters. She takes food from anyone very gently and will let me scratch her head but she will not perch. I spend time with her daily -talking and holding my arm inside the cage. She has no interest in perching at all, but she does enjoy regurgitating food on my fingers. I read that this is a sign of affection. Any suggestions on how to eventually get her to perch? Any other advice would be much appreciated also!