FaunaClassifieds - New croc skink laid a surprise egg. Help!

My (college-aged) son brought home his first red-eyed croc skink last Tuesday, named her Sebek, left her alone in the enclosure (bioactive paludarium) all day Wednesday to relax in her new home, and, when he went to feed her on Thursday morning, found an egg. That's how we know she's female. He had a lone bearded dragon for a decade, so this is somewhat new territory for the household. Temps are 73F to 80F on the ground, 85% humidity.

My questions:

1) If the egg is not fertile, how many days will it take to start showing signs of rot or whatever? It's been almost seven and it hasn't changed shape. We've been leaving it alone where she laid it since croc skinks do care for their eggs.

2) Traveling first from breeder to the pet shop, then from the pet shop to our home is obviously stressful for her. Being gravid at the same time likely made it worse. We are keeping a close eye on her physical appearance, which is in keeping with the many, many pictures of healthy croc skinks we've seen. She appears to be going about her normal lizard business in terms of eating well and defecating. Is there anything specific we should be looking for in case she needs further care?

3) She's eating small crickets and soldier worms right now. Are there any additional dietary needs for post-gravid females?

4) We understood that she would be a little over a year old. She's about 5 to 6 inches long, snoot to tail. Can a croc skink lay an egg that young?

Are there any questions we should be asking but haven't thought of? We're most interested in making sure she has a good, healthy start here.