I just started taking the pill (Mircette) 12 days ago and I am still having my period. I understand that because of the increase in estrogen my period might go a bit longer, but how long is it suppose to be? It is usually no longer than 5 days.

No, you are most likely still bleeding (called "breakthrough") because the estrogen level is significantly lower than your natural cycle, so your endometrial lining is unstable and keeps "leaking". This should resolve in another cycle as your body adjusts, or you will need to be put on a higher estrogen pill.