settings on iPhone to avoid charges when travelling question about carrier

Based from my carriers for my country, to be able to connect to an overseas carrier (to receive calls or sms from your home country) it can be enabled by contacting the carriers; with or without a charge.

Then, the carrier can be set to automatic/ON (connects to an overseas carrier automatically that is prefered by your home country's carrier) or OFF (choose the respective carriers that you prefer).

It is still best to switch off the cellular data when you're overseas.

Just a precaution:

Go Settings > Mobile/Cellular > Data Roaming > OFF

Data Roaming: Uses mobile data when you're connected to an overseas carrier (heavy charges apply).

Hope it helps.

If the device is set on Airplane mode, all radios will be turned off, you will have to turn wifi back on manually. With all the radios off, you will not be able to receive an SMS. If you have an unlocked phone, you can use the device with a local SIM card, however that would not reflect your number, so you would not get any SMS sent to your phone. Depending on your iMessage settings, if you have it set to receive on Apple ID, you could receive an iMessage. But with the device on Airplane mode turning off Data Roaming and/or cellular data is not necessary.

It depends on where you are. In the US, carriers charge for incoming and outgoing text messages. International texts differ slightly depending on the carrier. But, as you suggest, contacting the carrier is not a back idea.

You should not be charged by receiving a text message.

Check from your carrier again to confirm.