Hi Dry!
Sorry for my late reply.
Many thanks for all of your help! I really appreciate it. 
Looking at the error log, I do not see anything related to these notices.
I just installed and enabled it on our test server, and was able to reproduce the same error.
Steps:
1. Installed/enabled ext.
2. Navigated directly to page with CAPTCHA.
3. PHP notices appear.
I then went back to the ext. settings, and filled-in all the questions/answers, and the page loaded without problems.
Next, I went back to delete a few of the Q/A, and the page loaded just fine.
I was able to reproduce the notices again, by re-installing the ext., and then immediately visiting a CAPTCHA page.
Next, on our test server, I re-installed the ext. and then filled in a few questions… I then navigated to a CAPTCHA page and I did not receive any notices.
Lastly, I re-installed the extension and logged out of EE. I then navigated to a CAPTCHA page and received a blank page after about a minute of waiting. I assume this is because of the Output and Debugging Preferences of “1: PHP/SQL error messages shown only to Super Admins.”
So, in conclusion, it looks like if you are a complete noob and do not fill out any questions right away, a CAPTCHA page (at least this happens on our servers) will generate PHP notice messages.
Hmmm, maybe the ext. could fill-in the first Q/A with a default question/answer?
Let me know if you need more info!
Thank you!
Cheers,
Micky