Synology NAS do indeed have NFS support. In addition to enabling the protocol in settings, you may have to set NFS permissions on your shared folders in DSM (go to System Settings, then Shared Folders, select one and click Edit, then you have an NFS-Permissions tab).
As already hinted at, never enable SMB v1 on any device, as the encryption of the SMB v1 protocol has been broken a long time ago and your devices will be wide open for ransomware and other attacks.