Website Verification and Passwords.

Is there a way to send a request or verification ticket to either the company's website or Mozilla for SSL certification? Like, sending a link to DigiCert Inc. or Google Inc. Authority? I want to be sure that my connection to the website is private and secure. Furthermore, if the web page does not provide an SSL certification or verified website approval, would the passwords that I saved through Mozilla Firefox password manager be compromised or will they be secure even visiting a website that has no SSL certificate or verification? Please answer these two questions as soon as possible. Thank you.