mg/dl (milligrams per 100 milliliters) and mmol are essentially the same, just expressed in different values. As you've found out yourself, just take mmol times 18 or divide mg/dl by 18 to get the respective results.
The hbA1c (or A1c) test measures glucose that has stuck to your red blood cells. As red blood cells live 2-3 months, that delivers an average reading for the last 2-3 months. The results are different as it measures glucose on a different medium, but they can be converted (see the chart I linked below).
More experienced members can feel free to correct me, but my understanding is that if you measure for 3 months on a daily basis and take the average, it should be roughly the same as your A1c reading after that same time.
The chart here might help you, it certainly helped me:
http://www.diabetes.co.uk/what-is-hba1c.html