Can I make it so that random people off the Internet can’t just click on my profile, view it, and look at the posts I’ve made/threads I’ve started?
Or even, can I make it so that even people who have an account can’t do that?
Your CC profile sits behind a log-in screen, so Google does not index it (though your posts will be indexed). As for hiding your profile from other members, this is not currently an option, although you can decline to complete any identifying fields.