When your buying a house, you pay for heat. Unless its a condo or a coop, then it may be covered by monthly maintenance.
Gas or oil? Its about preference & cost. As of late gas tends to be less expensive. Washer/ Dryer may come with the home purchase. It all depends if the seller is leaving them behind or not.
Internet is usually your responsibility when buying a property.
Call me if you have any additional questions.