To navigate to the Messages section of your settings:
Open Settings > Preferences > Phone > Messages
You can then toggle ON / OFF the various messages options.
You can disable messaging entirely on the Light Phone II from the settings. When you disable messaging, you will not be notified of new messages and they will not be displayed in your recent activity. You will not have the option to send messages to contacts or numbers that you dial.
NOTE: There is not currently a way for a parent to disable messaging from the User Dashboard, it can only be disabled from the phone itself.
The Light Phone II is able to receive emojis in black and white for incoming messages. There is also the option to send a limited selection of emojis as well.
When Display Emojis is disabled, you will still receive all of your incoming messages, but all of the emojis will be removed. Incoming texts that only include emojis will appear as blank messages under the timestamp. Incoming messages that include emojis and words combined, still display all of the words from the message, with the emojis removed.
Disabling Group Messages means you will not be notified of messages from group threads. Group threads will not appear in the recent history and you won't be able to send group messages.