Can I renew my Retirement Visa (Non Imm-O) 45 days before expiration, and do I need an appointment to visit the Bangkok immigration office?

you aren't renewing anything 😮 you're applying for a whole new yearly extension (just like people do every year, year after year 🙂 ) that's why the documentation is the same because it's a new application 😉

You can apply for a new extension when you have 45 days or less left on your current stamp.

You can walk up and queue up with the zombie horde and wait it out OR you can make an online appointment and show up 15 minutes before the time and get seen without queuing, the choice is yours

Here's where you make an online appointment