Yes, there are character limits for Fill-in-the-Blank and Open-Ended questions.
Fill-in-the-blank is for shorter answer questions. The character limit for Fill-in-the-Blank questions is 160 chars. A message is displayed when the answer exceeds 120 characters.
Open-Ended questions tend to have longer answers. Accordingly, the character limit for Open-Ended questions is 1000 chars. A message shows up when the answer >800 characters.