Not sure why I couldn’t figure this out but I finally got my answer on how to place hyphens and underscores into URLs that I was typing into the Kindle’s basic web browser. Hit the SYM key (right next to the HOME key in the bottom row and a list of symbols pops up along the right side of the screen. Select anything from a dollar sign to a curly bracket and you are good to go!
Blessedly, the designers anticipated the need for the @ and / characters–these occupy their own keys on the physical keyboard.
Also, when the input box pops up for you to input a note or other text, there are several options for special characters shown across the top of the box. Each requires that you press the ALT key and another key to create the special character. ALT+6, for example, creates a question mark, ALT+8 a colon, and so forth.