Can a thyroid imbalance effect the rate of matabolism of alcohol? If a thyroid imbalance may cause you matabolism to increase, would the same thyroid imbalance also produce more ethonal from less alcohol consumption?

No. Alcohol is metabolized at a fixed rate by enzymes in the liver that are not affected by thyroid changes.
No, . No, that is a good question, but there is no evidence in the scientific literature that shows that thyroid imbalance affects ethanol metabolism.