Regarding option C.
Can we mount EFS on-premise without Direct Connect or VPN? https://aws.amazon.com/about-aws/whats-new/2018/10/amazon-efs-now-supports-aws-vpn-and-inter-region-vpc-peering/
Secondly is it good solution design (from exam point of view) to run NFS/EFS over internet?
Aravind is right that NFS likes to have a pretty stable and fast network connection. AWS used to say you could only use EFS remotely if you had Direct Connect, then they adding in a VPN connection as well. From an exam point of view, you are more likely to get a question on DataSync with EFS or S3. Probably worth getting familiar with that service and how you might use it to keep on-prem volumes in sync with EFS.
I personally would not use NFS over a WAN link as any sort of slight disruption could corrupt a file transfer activity. I’d probably go for Storage Gateway or DataSync instead that’s more designed to be async.