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Did the vet say anything about the black flakes?
I think an X-Ray would show any sizable rocks very clearly.
If she's not eating, then I wouldn't expect much waste.
I would not force the syringe deeper, did you discuss this with the vet? Did they do a demonstration.
They can swallow when out of water but usually don't because it's difficult. I would keep up with the Pedilyte soaks with pellets.
Som other thoughts...
I would bump up the water temperature to 80F. Skip the water conditioner and use some carbon filter media. Look into a 5.0 UVB light. Look into a better basking area if she can't dry off.