1. Will I pay for 100GB in Warm storage and 50TB in cold storage or the data referenced by the second backup will be kept in warm storage and I will pay 50TB Cold + 50TB Warm + 100GB warm?

According to reference [1] under Lifecycle, each backup to cold storage will be a full backup. This means that when you transition the 1st backup to cold storage, 50 TB will be charged as cold storage. Because the 2nd backup is incremental, whatever data that the 2nd backup references from the 1st backup will be kept in warm storage.

2. And so, will my incremental backups store just what has changed even if my full backup is in cold storage?

AWS Backup will keep data that is needed by other incremental backups as needed. This means that even if the 1st backup of EFS was deleted, the data that is referenced by the 2nd backup and subsequent backups will be kept to ensure that those backups can be restorable.

References

[1] Backup rules - https://docs.aws.amazon.com/aws-backup/latest/devguide/creating-a-backup-plan.html#backup-rules

Per https://docs.aws.amazon.com/efs/latest/ug/awsbackup.html

AWS Backup automatically transitions data to cold storage only for data that no longer exists in the most recent warm backup. For example, your file system has 100 files when you create a backup and you delete two files the day after you created the backup (100 files - 2 files = 98 files on second day). When you transition the data to cold storage, only the two deleted files move to cold storage and the remaining 98 files are billed as warm storage.

So in your case there would be 50TB in warm storage, as that is the size of the data in the 2nd recovery point (i.e. if you did a full restore you would expect to get 50TB of data). You say 100GB has changed, therefore there will be 100GB of data that is only in the 1st retention point, and this will be eligible for transition to cold storage.