The last item, that your benefit amount is fixed at the age 62 amount, is mostly true (but you could request payment of the age 63-66 unpaid benefits to be paid when you go to SSA and apply again). If you choose not to collect retroactive benefits, I believe your monthly benefit will be increased for not only the repaid benefits from age 62 (if you were working), but the unpaid age 63-66 benefits will act to increase your monthly benefit.
One cautionary tale regarding different representatives and their different opinions. Unless you have given a complete review of your fact pattern to each of those representatives, their opinions can't be compared directly. A simple turn of phrase, or omission in what you disclose to the next representative, must use their exact terminology and a complete fact pattern. It's why in my business I drop customers who have shopped opinions. Not that they received bad advice, but I find I spend a lot of time correcting what other people might have opined. And, you are left with not knowing who to believe.
It's best to go to their office, scheduling an appointment, and reviewing your entire case with the same case worker. That way, one person reviews your entire case file and advises.
Thanks for asking your questions at Just Answer. I hope this shed some light on your situation. Positive feedback using our rating scale is appreciated. I'm PDtax.