Suspicious Traffic

This sort of thing (A and B) is common and normal, there's no need to take any specific action (and fail2ban isn't useful for this sort of thing unless they're hammering you). B probably didn't return any error because it's probably a valid request with invalid parameters; you probably do have /index.php, and your script is probably just ignoring the pareameters.

For C, that looks like a completely normal web request. Somebody using Chrome tried to access your website. Why would you want to block it?

Thanks for the reply Guspaz!

Yes, I do have index.php.

Well, I probably should have stated that I'm new to managing this aspect of a server, so I just wanted to check. You've definitely put me at ease though. In regards to C, I had figured that legitimate requests would have had more than '/' - something along the lines of B.

If they're accessing your site for the first time in a session, like at "http://mydomain.com", they don't have any extra parameters to pass.

A and B are definitely malicious traffic, but if you keep up to date with security updates, you should be fine.

I update pretty well, so I guess that's covered.