Both of these statements are false. Nominal GDP is simply the market value of all final goods and services produced in a given country in a given year. This means that nominal GDP can go up just because prices go up, even if the country does not actually produce more things than it did in the previous year. Real GDP takes inflation into account. Thus, if there is inflation, nominal GDP can go up even as real GDP remains the same or drops. This is not common, but it is possible.
When you have a positive GDP gap, you actually have inflation, not unemployment. A positive GDP gap means that the economy is producing more than it can sustain in the long run. Clearly, a country could not be producing “too much” if it had high unemployment. As the size of the positive GDP gap increases, you would get more inflation and less unemployment.