In modern data center architectures, an overlay network is a logical or virtual network built on top of an underlay, where the underlay is the physical IP fabric that provides basic Layer 3 transport and reachability between fabric nodes. The overlay abstracts the physical topology and delivers tenant connectivity and segmentation services. This makes the statement that an overlay is a virtual network running on top of a physical network correct.

In EVPN VXLAN based data centers, overlays commonly carry both Layer 2 and Layer 3 services. Layer 2 extension is achieved by encapsulating Ethernet frames inside VXLAN so that a VLAN like segment can span multiple leaf switches across a routed underlay. Layer 3 services are delivered either through symmetric routing at the VTEPs or by advertising IP prefixes and host routes through the overlay control plane. As a result, overlays are not limited to Layer 3 traffic only, and statement D is correct.

The overlay is not defined by being public versus private. It can be built for private multi tenant segmentation inside a single data center, across multiple data centers, or to connect to external services, but public network is not a defining attribute.

Verification sources from Juniper documentation

https://www.juniper.net/documentation/us/en/software/junos/evpn-vxlan/topics/topic-map/evpn-vxlan-overview.html

https://www.juniper.net/documentation/us/en/software/junos/vxlan/topics/topic-map/vxlan-overview.html