>> Is there a way to set up a text box so that it expands when needed (when more text is entered)?
You could try to to use a Textfield (Multiline) field. Form filler will be able to scroll up/down if text goes beyond the input box height.
Another way is to size the Multiline field in FormsCentral/Design Tab during authoring to a reasonable size which you think will be enough for the user's text input.
Hope this helps,