Awww, thanks for giving this beautiful girl a home

I have an ancient leopard gecko, I'd imagine care would be fairly similar.
First, since she is molting make certain you are misting her habitat, which will help the skin come off easier. Also, do NOT remove the shed skin right away. Allow her the opportunity to eat it, which geckos almost always do as their shed skin is a good source of nutrition for them. Also, my leopard gecko sheds every month like clockwork. A healthy gecko should shed pretty frequently. A broken tail will grow back, but will be stumpier than the original and may appear slightly deformed. This is normal. Keep an eye on the stump as it heals and observe for signs of infection, but if it scabs over nicely and shows no signs of infection, just let nature take it's course. Personally, I prefer reptile carpet to any other bedding. Leo almost died from being put on sand as a juvenile (every time he ate a bug, he ate sand too and it effectively cemented his insides together). Ever since I will use nothing but the special carpet. I also refuse to use under tank heaters and prefer heat lamps in appropriate high heat fixtures. Too many horror stories of those under tank heaters catching fire. All prey should be gut loaded for several days before feeding. Gut loading is basically feeding the insects highly nutritious food, which should be a combination of produce and commercial gut loading pellets. This insures the insects are full of nutrition. I am not familiar with crested geckos, but some general things to look into would be:
-Active during the day or a nocturnal species? This will help understand her natural behaviors better. A nocturnal gecko may come out every so often to bask under their sunlamp, but will mostly sleep during the day and it's normal. A day active gecko who's sleeping excessively during the day may be ill.
-Environmental needs (climbing? vines? rocks? Long tank or tall tank? etc...)
-Heat and humidity needs. This is VERY important to maintain good health, digestion, shedding, activity levels, appetite etc... Reptiles are very sensitive to environmental conditions. Some may also need a heat gradient in their enclosure where there is a very hot area and a cool area so they can self-regulate their body temperature.
-How often to feed. I know of no reptile that should be fed daily (no matter what places like Petco may say). Overfeeding can lead to early death and health issues. My gecko eats once or twice a week or so, less frequently in the cool months.
-Does this species need calcium dusted prey. Many reptiles are prone to calcium deficiencies and need supplemental calcium.
One last thing, some vets may look over a reptile, but finding a vet who specializes in/cares about small reptiles will be next to impossible. Not many people are willing to take a $20 lizard to a vet. Make sure you are familiar with signs of illness, but in general a healthy reptile being properly cared for will never have to see a vet.
Edit: One last last thing

Geckos can be extremely long lived when properly cared for. My old guy is at the end of his life at 20 and I don't honestly expect him to live too much longer. But a 5 or 6 year old gecko is still quite young with a lot of good years ahead!