It sounds like you need to do more research in terms of appropriate husbandry. Everyone here who keeps leopard geckos will have different answers to the questions you asked. It’s important that you read recommendations from many different sources and make your own decisions once you have educated yourself.
First- read all of these. Ideally seek out more on your own as well. All of them have their own bias:
- A care sheet from a very reputable hobbyist source
- A care sheet from a reputable exotics clinic
- A care sheet from a reputable breeder
- A care sheet from a big feeder insect company
- A care sheet from a large breeder of leopard geckos
- A care sheet from a hobbyist magazine
Second- give us enough details to answer your question. Surface temps on hot & cold sides, heating source, how you read your temps (probe, gun, etc.), humidity, cleaner crew you have in there, substrate, cage set up, diet & schedule, lighting, caging used, etc.
tl;dr : (1) No, it’s not normal, something is probably wrong with your husbandry. (2) Crickets that are appropriately gut-loaded (not just powdered) can be acceptable, but should never be left uneaten in the tank, as they can eat your gecko.
edit: I forgot to add that you should search this forum and read through the many times similar questions have been answered.