Yes, it's possible for a female to lay eggs without being bred, similar to a chicken. Check their bellies every month or so to look for pink circles, if you see them then put a container of moss or bed a beast in their tank to lay the eggs in, then toss out the eggs when they lay them.
Feed as many crickets as they'll eat in one sitting. I personally, when I did feed crickets, would put some in over night and in the morning take them out. I had some shy eaters that wouldn't eat in front of me, or if I was in the living room (where I house them).