Am I being charged for international texting?

So I am doing a masters program in Ireland, so I'm international. Everyone that I talk to back home has an iphone just like I do, and I have a question that I cannot find an answer to.

Since I'm in Ireland, I don't want to have a huge phone bill every month, so I have all forms of roaming off (voice, data, and international CDMA). I also have Cellular data off, as well as MMS and SMS messages.

I've checked under the current data usage period, and current period roaming, and the data usage is 0 . When my friend back home texts me, he says that they are sending to me as regular texts. He receives mine as regular texts as well unless I'm in a wifi area, then we are both send and receive them as Imessages.

My questions is that even with all roaming turned off, cellular, ect, I'm still able to send and receive text messages while I'm NOT in a wifi area. This only works for my friends and family that have Iphones, so I'm assuming that it means I'm okay to text them while I'm not connected to wifi?

one thing to mention, that since I'm in Ireland, my service provider at the top left of the screen no longer says AT&T. It says "Vodaphone IE" and sometimes changes to other names like Meteor, O2, and a couple others. My plan is still through AT&T, so i'm not sure why it changes over to those. Maybe that's why I'm able to send texts?

I just don't want to rack up a huge phone bill, not knowing I was accumulating international charges. Because if everything is turned off except for Imessage, and the data under cellular in settings isn't going up, then theoretically I'm not using data right? or that it should be free? I've been here about a month, and my mom pays the bill. She hasn't called to say that the phone bill was extremely large, but I don't wan't to text if there's some kind of risk. That being said, I would really appreciate some help with the above scenario that I just described, because this has me clueless.