Fetion can send text messages to mobile phones, right? ?

Yes, I often do. In this case, the other party doesn't charge, because he does, and you don't charge, because you use Fetion (if you send it by mobile phone, you still charge for traffic).

However, there is a premise that he replied "Yes" when you sent him an invitation for the first time, otherwise, you can't send him an airmail. Probably this is done to prevent abuse, resulting in too many spam messages.