What makes it complicate is that in Software Defined network like SDA, they took the current network and call it underlay and then, using software, they build a upper layer they call Overlay. At the end, this is all the old and good TCP/IP over Ethernet but this overlay layer makes it confusing.
"So, in SDA, where is this Layer 2 VNI coming from? My understanding is, there is no Layer 2 VNID in SDA."
Yes, in fact there is, althouth is not mandatory. Take a look on the picture I attached. It show perfectly well how this is done.
"Also, if the traffic is routed from one subnet 10.1.1.0/24 to another subnet 10.2.2.0/24 (within the same VN), the VXLAN encapsulation would be IP-in-IP, right?
If traffic is switched within the same subnet 10.3.3.0/24, but across two switches, the VXLAN encapsulation would be MAC-in-IP, right?"
Keep in mind that inside the fabric is like we have only on switch and the encapsulation is always over IP. Take a look on the picture attached again.