Is there a way to view the text messages my child is sending to his friends?
Unless you install a third party app which would also send a copy of the text to another location, then the only way to view the messages would be to look at the phone.
Third party apps which will do this are available for smartphones, but I am unsure whether or not they are available for feature phones.
ask to look at the phone
compare the list on the phone with the date/time/number sent/received on your verizon bill
if any are deleted/not showing turn on your parenting module
(it may be a good idea to leave this on until the child is 18)