I know of no character limit, nor a way to set one.
A textbox is limited to being on a single page but you can link them so that text in one can flow into another.

Consider using a UserForm which would let you do the things you want.

• Create a Simple Userform by Graham Mayor, MVP
• Create & Employ a Userform by Greg Maxey

The term text box as used above refers to the graphical element you get under Insert> Text Box. It does not refer to a text formfield or a plain text or rich text content control. The advice to consider a userform, though, does apply to those. A userform is a custom dialog box that can be used to get information from the user or otherwise control a Word document.



See also:

• Making Forms with Microsoft Word
• Create a Form Using Word Content Controls by Greg Maxey
• Create forms that users complete or print in Word - Office Support

Those pages are about on-screen forms that mimic or produce paper forms. They are documents formatted to take information. UserForms and these other document formats can be used together.