1. Does all the VTEP network(overlay network) should be in the same vDS portgroup and VLAN ID? If the overlay network is a L3 network(cross L2 network), how to deal with the VLAN ID?
VTEP is nothing but a VMK network on ESXI host which is capable of encap/decap of VXLAN packet - Do you have multiple clusters and are you having unique DVS for each cluster ? . For eg if you have VDI and vSphere worload cluster it is always better to have unique DVS for these clusters and VTEP/VTEP's on each host can always communicate between/across the clusters and sites as long as you have a L2/L3 connectivity with or without a VLAN.
2) Can i create one VXLAN logical network cross multiple vDS ? Suppose these vDS are in the same NSX transport zone.
Yes,transport zone is the decision factor for that.Ensure you add the respective clusters to whatever transport zone they want to be a part of.