No, that's simply untrue. They're completely unrelated. You can use cookies from PHP or, I think, send them in HTTP headers directly. ReCAPTCHA does something different, true. It uses Javascript. I believe it still uses sessions or something like sessions, though. I can't remember the details.
There are OCR programs to read text from an image. I don't know how many bots actually try that, but, yes, that's why the letters are obfuscated.
Well, it's still a lot more work than just creating a text-only bot that reads HTML pages.

