is the hba1c a fasting test

Not that I've heard. Most bloods taken are fasting. I would check again. Ask what test it is.
Always ask your team to explain everything.

There are several blood tests.

Fasting blood glucose is taken in the morning, before breakfast, after fasting since the night before.
Oral glucose tolerance test is 2 tests, 2 hrs apart, after fasting since the night before
Hba1c can be taken at any time of day, no need to fast - it gives an average of your blood glucose over the last 2-3 months

Cholesterol is often taken.
A fasting cholesterol test is the most informative.
Non-fasting tests are of limited use (but are cheaper!) and are often affected by fats that you ate in your last meal.

It's always worth checking whether you need to fast, or not. If nothing else, worth trying for an early appt so you don't suffer starvation all morning.

Hope that helps!