I know you are doing a great job, you took great care in setting her up, the Powersun is just not that strong unless the beardie is basking about 8-10" below it for hours. Another thing to consider is that some babies are more predisposed to calcium issues depending on the health of the mother as well as the care received before you got it. So there's no fault on your end. Those sand mats are a newer item, most people using them end up taking them out. I'd take it for a refund if you're able.
And no, their nails won't get long until they're a bit older and as long as you have a few good climbing rocks in there it will work out fine. Oh, and it would be good to feed her twice a day, use calcium WITH D3 twice a week. Is her appetite pretty good ?