Does Metro Ethernet support multiple VLANs which are in the two different location?
In site A
There is one Metro Ethernet link up site A and Site B.
If so, how to route the local LAN traffic to Metro Ethernet?
I can't answer for him, but you can share the same subnet over a MetroE link.
To reiterate, treat a MetroE link like a physical link between switches. MetroE will be transparent to your L2/L3 design as you can extend these L2/L3 domains over the MetroE connection.
On your design, you need to take into account overlapping IP address assignment thus if you had a DHCP server on Site A handing out addresses and another on Site B handing out same addresses, those issues need to be corrected - same goes for static IP address assignment.
Any Network Engineer would spot this issue during the design but I believe it's worth mentioning for clarity.