You'll have to look at your rental agreement and see if it says you have to pay rent and utilities. Usually it's all part of your rent, but some do charge extra for utilities. You should have been told that up front.
Is a landlord allowed to charge me extra for electric and extra for ac/heater on top of my rent?
Yes, if it's part of your agreement. Hopefully you have one in writing. If you don't, and you've been living there for a while already and the landlord had simply added it, then no .. There are very struck laws in terms of rental increases once a tenancy has already begun. You will then have to check with your local tenancy laws.
You need to read your lease. My niece lived one place that the utilities were included in the average month. But if he went over the allotted amount, used more electricity or water, he had to pay more for those months. Even if he used half that amount every other month.
