Does it cost to receive a call from abroad?

Yes, it is pretty expensive. Normally both parties pay the price of the call. Ask your cell network for the rates while 'roaming'. But it depends on the country and carrier. In Australia there is no charge to the called party for incoming calls. This is because you can't be charged for things you don't originate or have control over. Therefore, you can be called from anywhere in the world without charge. If you take your Australian cell phone to another country - then you start to incur international roaming which will cost.