I've prediabetes (fasting 91 mg/dl, hba1c5.7%) no ketone in my urine. Why I have diabetes synonym like dry skin, urination, my weight loss 6 kg in a month?

Insulin resistance,, You likely are developing Insulin resistance where the sugar isn't getting into your cells but is remaining in the blood stream and causing the symptoms. Your glucose is not high but might have increased from your original baseline and your hba1c is borderline so it's likely sugar is in your blood that should be processed by your body so see dr for more tests, diet, and type ii diabetes meds.
See details. Your current levels of glucose and a1c are normal. It is unlikely your current symptoms are related to any prediabetic condition.