No, you have no options.What are my options here? Do I have any options?
What you should have done was give your move out notice for the lease expiration with the proviso that you'd renew if the carpet got replaced before you signed any renewal.
Your power was in your hand (your signature). Once your signature left your hand, no more power.
Yes.Can a landlord or its agent refuse a request to replace an 8-yr-old carpet?
Yes.Also, can the landlord refuse to give me installation proof / invoice?
If he ever tries to charge you for the carpet and you end up in court, then he'll have to present it.
I hope you took pictures of the carpet and the rest of the premises when you moved in. If not, take them now, and again when you move out.
At next renewal, tell your LL that you'll be moving if he doesn't replace the carpet before you sign for the renewal. If he balks, move to a place with better flooring.

