I live in a 4th floor apartment. Found a praying mantis on my living room floor which apparently came in when sliding door was open. I think it's a Chinese Mantis after looking at photos. I placed it in a large container with twigs and gave it a few bugs to eat each day, keeping it just until I could take it to my mom's house where she wanted it to lay eggs in her garden. Well....I waited too long (12 days) and it just laid an egg case on a twig in the container yesterday. Didn't plan to keep it that long. Was waiting for warmer weather reports at night and no storms when I transferred her. 
My questions are:
1. Is it most likely she mated before entering my apartment? I hope so. Otherwise the eggs wouldn't be fertile, if I understand correctly?  I read that they still lay eggs even if haven't mated. Hopefully she mated then was finding a warm place to lay the egg sac.  
2. Is there a way to identify if the egg sac contains fertilized eggs?  
3. Does a mantis only lay 1 egg sac or could she lay more?
3. If it might be fertile I want to give it the best chance possible of hatching when spring arrives. Should I just go ahead and put the twig in a bush by the garden or is it better to keep it in the container in a cool place like an unheated patio til spring? I also heard refrigerator.?
3. If she is kept indoors, is there a chance  she would live til next summer, mate, and lay another egg sac? I know that those living outdoors die soon after laying egg sac but indoors can live up to a year and a half if taken care of and fed.  
I know I should have transferred her to the garden sooner. I read that they don't lay egg sacs til end of fall so I thought I had time.  It was intriguing to watch and I wanted to show nieces for a learning experience. But now I wish I had just taken her over right away. I'm almost "attached" to her in a way (and my cats too..lol) although I haven't tried to let her walk on my hand because she creeps me out when she turns her head and looks straight at me and she seemed agitated the times I did have my hand close to her in the container.  I found out people keep them as pets. I hate to put her out knowing it will be cold soon and she'll die. But I read they only live indoors a year and a half at the most. Maybe could give her to an elementary school to take care of. 

Any thoughts would be appreciated, especially if you think there's a good chance the egg sac is viable. 

Thanks!