AWS Backups Malware Scanning Threat analysis & containment Methodology

Hello.

Where can the user find the historical scanned results performed on EBS/EC2/S3 snapshots/recovery-points?

You can check this in the AWS Backup console under "Malware protection" → "Malware scan jobs" screen.
I think you can also access this information using the ListScanJobs/DescribeScanJob API.
https://docs.aws.amazon.com/aws-backup/latest/devguide/malware-protection.html

How does the quarantine process works for flagged resources with threats identified?

AWS Backup / GuardDuty does not have a native "automatic quarantine" feature.
The service's responsibility is to scan and return THREATS_FOUND/NO_THREATS_FOUND; I believe that subsequent isolation and restriction should be handled by a custom architecture using EventBridge and Lambda.
https://aws.amazon.com/jp/blogs/storage/scan-backups-for-malware-with-amazon-guardduty-malware-protection-for-aws-backup/

Would the AWS Backup Automatic Restore testing selects or eliminates the flagged snapshots during the next schedule?

I don't think it will be excluded because there are no filters based on malware scan results or tags.