Request to remove all cost related services

Hello.

a) Route53 - should I delete my domain name to avoid costs generated for this service? If so, what will happen to the domain name which is still valid and not expired? Please advise, what should I do in the future if I want to retain this domain name?

Route53 charges fees for hosted zones and records.
If you delete this, you will no longer be charged for hosted zones or records.
https://aws.amazon.com/route53/pricing/?nc1=h_ls

When deleting a hosted zone, please note the following documentation:
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/DeleteHostedZone.html#delete-public-hosted-zone-stop-routing

If you delete a hosted zone, you can't undelete it. You must create a new hosted zone and update the name servers for your domain registration, which can require up to 48 hours to take effect. In addition, if you delete a hosted zone, someone could hijack the domain and route traffic to their own resources using your domain name.

If you delegated responsibility for a subdomain to a hosted zone and you want to delete the child hosted zone, you must also update the parent hosted zone by deleting the NS record that has the same name as the child hosted zone. For example, if you want to delete the hosted zone acme.example.com, you must also delete the NS record acme.example.com in the example.com hosted zone. We recommend that you delete the NS record first, and wait for the duration of the TTL on the NS record before you delete the child hosted zone. This ensures that someone can't hijack the child hosted zone during the period that DNS resolvers still have the name servers for the child hosted zone cached.

Also, if you purchased your domain with Route53, disabling automatic renewal will prevent the next renewal from occurring.
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-enable-disable-auto-renewal.html

If your domain has not expired, you may want to consider moving to a free DNS service.
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/DeleteHostedZone.html#delete-public-hosted-zone-stop-routing

If you want to avoid the monthly charge for the hosted zone, you can transfer DNS service for the domain to a free DNS service. When you transfer DNS service, you have to update the name servers for the domain registration. If the domain is registered with Route 53, see Adding or changing name servers and glue records for a domain for information about how to replace Route 53 name servers with name servers for the new DNS service. If the domain is registered with another registrar, use the method provided by the registrar to update name servers for the domain registration. For more information, perform an internet search on "free DNS service."

b) EC2-Other - I cannot figure out if any service is used under this name, but there is a small cost still showing.

"EC2-Other" includes EBS charges, EBS snapshot charges, etc.
So please check if there are any EBS, snapshots, etc. left.
https://aws.amazon.com/blogs/aws-cloud-financial-management/tips-and-tricks-for-exploring-your-data-in-aws-cost-explorer-part-2/

In the past, many financial analysts and DevOps engineers have asked for more context into specialized aspects of EC2 service usage. They cite one of these service categories as particularly helpful—specifically the EC2-Other service category. The EC2-Other category includes multiple service-related usage types, tracking costs associated Amazon EBS volumes and snapshots, elastic IP addresses, NAT gateways, data transfer, and more.

Also, if I delete my entire account, will it help to avoid any cost if that is the best or fastest option?

Yes, if you close your AWS account, it will become completely unusable after 90 days and you should no longer incur charges.
https://repost.aws/knowledge-center/close-aws-account