Taking out sim cards and cellular data on iPhone 4s?

Currently I'm in a different country and do not want any unexpected charges to pop up on my bill when I return. My sim card is out but I still send emails and browse the internet using the local wi-fi from my location; since the sim card is out, I won't be charged? Also, what is cellular data? Like I said, I took out my sim card and data roaming is disabled but cellular data is turned on, I won't be charged for it being on since the sim card isn't inserted, correct?

No, you will not be charged. Your not using your SIM which tracks everything you do so you get charged so you won't be charged. If your using the local Wi-Fi, your good.