I finally got it working after weeks of struggle.
I'm from India and have previously tried using multiple cards and even a US credit card to complete the purchase but it didn't work. I can't use the developer app to enroll because enrollment is not yet available in my country through the app when posting this. Like everyone else, I was frustrated at this and I would suggest not showing your frustration in the emails you write to Apple Support because they will ghost you after 2 emails just like they did to my previous Apple ID. If they do ghost you anyway, try to make another purchase and create a new support ticket.
I made a new Apple ID and linked my card to it. Then I bought a song from iTunes to show as evidence when the support asks for it and purchased the license. Use the following link to check the status of your order and wait for it to show as canceled
https://secure4.store.apple.com/shop/order/list
I wrote to support and told them about the problems until they escalated the issue to a senior adviser after a lot of emails. Remember to be as polite as possible when you're exchanging emails. They asked me for my government-issued identity cards to verify me and my address. This must be crucial because I used my dad's credit card and not mine. The adviser tried to perform the transaction from their end and for some reason it got the work done. I did not give my credit card details over the email. They just performed the transaction from their system. When I checked from the link, I found out that my order was actually canceled and a fresh order from them was placed.
During this ordeal, I used a MacBook to create an Apple ID, add the credit card to my account, and purchase the song. Then as everyone suggested, I used safari for the enrollment and cleared the cookies, cache, and history beforehand.
My Apple ID was also new so you don't need to worry about finding an old one.
The new Apple ID was of the @icloud domain.
Remember: Be calm and collected at all times in emails otherwise they won't escalate your case to a senior adviser who has the magic wand.