Help me replace my AirPods!

I bought my AirPods Pro from Pakistan. Not from an Apple Certified Store as there aren’t any in my country. But I checked inputing the the serial number on the apple website and it is an original apple product and paid the original price for it too. There was a charging problem with my left AirPod from the beginning and at first I didn't think much of it and just re-adjusted the AirPod and after a few tries it did the trick. But slowly it started to get worse to the point when I would put the Pod in the case overnight and in the morning it would still be at 0% and still doesn't charge after 100 re-adjustments(BUT SOMETIMES IT WORKS MIRACULOUSLY AND LOOKS LIKE IT HAS NO PROBLEMS WHATSOEVER), and now it's been three months since the purchase and I still haven't been able to claim the one-year warranty. Finally, my brother is flying to England (couldn't go before because of COVID restrictions) and I will be giving him the product (with the original box) to get it checked and replaced from the Apple Store. Another thing to note is that, the Purchase Date on the Apple website has still not been updated since the purchase( I thought the seller would do it himself when i bought it but he told me yesterday that you were supposed to do it.). And also I don't have the receipt of the

purchase. 

So I had some questions: 

1) Does the following issue qualify as a 'defected' product (to which they should provide a replacement) and not a 'damaged' one?

2) Is the not updated Purchase Date be a problem? I've heard that 'Apple products' Purchase Dates are auto-updated after 90 days of use.' Is this true? Do they always know when the product was bought or is it just through the website: https://checkcoverage.apple.com

3) I've heard that 'After 90 days of purchase, Apple will not offer you a replacement and instead a repairing of the AirPods.' Is this true? Will I get a replacement (Like a new box and a new pair of Pods)?

4) Should I update the purchase date now? If so, am I supposed to put todays date or the date when I bought them? Regardless the One-Year warranty is supposed to cover the replacement right? 

5) Is it a problem that I haven't bought the product from an Apple Certified Store? 

6) Is there anything specific I need to know prior to go looking for an Apple Store? What Store do I go to? I heard you are supposed to go to a specific Genius Bar to claim a warranty. If so, do I need a reservation? an appointment?

Thank you so much for reading and helping!!!