Can I delete one message at a time, or does whole conversation delete
You should be able to delete single messages in almost any messaging app. Which messaging app are you using? If it's Verizon's Message+ app, then once you have a conversation open, you should be able to press and hold on individual messages for a pop-up menu that will let you delete those messages. You can also tap the menu button on the top-right and select "Edit Conversation," and then select multiple messages in the conversation to delete.
