Typically, phones will convert text messages into picture messages when:
On some phones you can clearly see when this happens - for example, you might see a character count changing to a file size.
Some phones let you switch this function off, or enable you to set up an alert when it happens. You'll need to check the manual or go to the support website for your phone to see to do.
The charge for MMS would apply whether your messages were going to landline or mobile.
If you would like to protect yourself from the risk of MMS charges I'd recommend switching it off in your phone settings.