Firstly, note that newsFile doesn't exist. It should never exist in a stock install. It is index 'news' and the File bit is always on the next line but for some reason when you copy from the error log it mashes things together.
That said, farting around with Subs.php isn't solving the problem - the undefined errors won't cause it to fail like that, simple as that. It might break the CAPTCHA, possibly, but it wouldn't cause a 500 on action=register.
Something is more fundamentally wrong, and I'd be looking at... Register.php and Subs-Members.php being compared to a stock copy from 2.0.2 to see what's different.